ti83Guidebook - TI-83 GRAPHING CALCULATOR GUIDEBOOK...

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Unformatted text preview: TI-83 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. IBM is a registered trademark of International Business Machines Corporation. Macintosh is a registered trademark of Apple Computer, Inc. Windows is a registered trademark of Microsoft Corporation. 1996, 2000, 2001 Texas Instruments Incorporated. Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. US FCC Information Concerning Radio Frequency Interference This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: Reorient or relocate the receiving antenna. Increase the separation between the equipment and receiver. Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. Table of Contents This manual describes how to use the TI.83 Graphing Calculator. Getting Started is an overview of TI.83 features. Chapter 1 describes how the TI.83 operates. Other chapters describe various interactive features. Chapter 17 shows how to combine these features to solve problems. Getting Started: Do This First! TI-83 Keyboard .......................................... TI-83 Menus ............................................. First Steps ............................................... Entering a Calculation: The Quadratic Formula .......... Converting to a Fraction: The Quadratic Formula ........ Displaying Complex Results: The Quadratic Formula .... Defining a Function: Box with Lid ....................... Defining a Table of Values: Box with Lid ................. Zooming In on the Table: Box with Lid ................... Setting the Viewing Window: Box with Lid ............... Displaying and Tracing the Graph: Box with Lid ......... Zooming In on the Graph: Box with Lid .................. Finding the Calculated Maximum: Box with Lid .......... Other TI-83 Features..................................... Turning On and Turning Off the TI-83 .................... Setting the Display Contrast ............................. The Display .............................................. Entering Expressions and Instructions ................... TI-83 Edit Keys .......................................... Setting Modes ........................................... Using TI-83 Variable Names ............................. Storing Variable Values .................................. Recalling Variable Values ................................ ENTRY (Last Entry) Storage Area ........................ Ans (Last Answer) Storage Area ......................... TI-83 Menus ............................................. VARS and VARS Y.VARS Menus ......................... Equation Operating System (EOS) ..................... Error Conditions ......................................... 2 4 5 6 7 8 9 10 11 12 13 15 16 17 1-2 1-3 1-4 1-6 1-8 1-9 1-13 1-14 1-15 1-16 1-18 1-19 1-21 1-22 1-24 Chapter 1: Operating the TI-83 Introduction iii Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using the Equation Solver ............................... MATH NUM (Number) Operations........................ Entering and Using Complex Numbers................... MATH CPX (Complex) Operations ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ....................................... TEST (Relational) Operations ............................ TEST LOGIC (Boolean) Operations ...................... Getting Started: Graphing a Circle ....................... Defining Graphs ......................................... Setting the Graph Modes ................................. Defining Functions ...................................... Selecting and Deselecting Functions ..................... Setting Graph Styles for Functions ....................... Setting the Viewing Window Variables ................... Setting the Graph Format ................................ Displaying Graphs ....................................... Exploring Graphs with the Free-Moving Cursor .......... Exploring Graphs with TRACE ........................... Exploring Graphs with the ZOOM Instructions ........... Using ZOOM MEMORY .................................. Using the CALC (Calculate) Operations .................. Getting Started: Path of a Ball ........................... Defining and Displaying Parametric Graphs .............. Exploring Parametric Graphs ............................ Getting Started: Polar Rose .............................. Defining and Displaying Polar Graphs ................... Exploring Polar Graphs .................................. 2-2 2-3 2-5 2-8 2-13 2-16 2-18 2-20 2-23 2-25 2-26 3-2 3-3 3-4 3-5 3-7 3-9 3-11 3-13 3-15 3-17 3-18 3-20 3-23 3-25 4-2 4-4 4-7 5-2 5-3 5-6 Chapter 3: Function Graphing Chapter 4: Parametric Graphing Chapter 5: Polar Graphing iv Introduction Chapter 6: Sequence Graphing Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes Combinations ............................ Exploring Sequence Graphs.............................. Graphing Web Plots...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI.82 Sequence Variables .......... Keystroke Differences Between TI-83 and TI-82 ......... Getting Started: Roots of a Function ..................... Setting Up the Table ..................................... Defining the Dependent Variables........................ Displaying the Table ..................................... Getting Started: Drawing a Tangent Line ................. Using the DRAW Menu ................................... Clearing Drawings ....................................... Drawing Line Segments .................................. Drawing Horizontal and Vertical Lines ................... Drawing Tangent Lines .................................. Drawing Functions and Inverses ......................... Shading Areas on a Graph ............................... Drawing Circles.......................................... Placing Text on a Graph ................................. Using Pen to Draw on a Graph ........................... Drawing Points on a Graph .............................. Drawing Pixels .......................................... Storing Graph Pictures (Pic) ............................. Recalling Graph Pictures (Pic) ........................... Storing Graph Databases (GDB) ......................... Recalling Graph Databases (GDB) ....................... Getting Started: Exploring the Unit Circle................ Using Split Screen ....................................... Horiz (Horizontal) Split Screen ........................... G-T (Graph-Table) Split Screen .......................... TI.83 Pixels in Horiz and G-T Modes ..................... 6-2 6-3 6-8 6-9 6-11 6-12 6-13 6-15 6-16 7-2 7-3 7-4 7-5 8-2 8-3 8-4 8-5 8-6 8-8 8-9 8-10 8-11 8-12 8-13 8-14 8-16 8-17 8-18 8-19 8-20 9-2 9-3 9-4 9-5 9-6 Chapter 7: Tables Chapter 8: DRAW Operations Chapter 9: Split Screen Introduction v Chapter 10: Matrices Getting Started: Systems of Linear Equations ............ 10-2 Defining a Matrix ........................................ 10-3 Viewing and Editing Matrix Elements .................... 10-4 Using Matrices with Expressions ........................ 10-7 Displaying and Copying Matrices ........................ 10-8 Using Math Functions with Matrices ..................... 10-9 Using the MATRX MATH Operations ..................... 10-12 Getting Started: Generating a Sequence .................. 11-2 Naming Lists ............................................. 11-3 Storing and Displaying Lists ............................. 11-4 Entering List Names ..................................... 11-6 Attaching Formulas to List Names ....................... 11-7 Using Lists in Expressions ............................... 11-9 LIST OPS Menu .......................................... 11-10 LIST MATH Menu ........................................ 11-17 Getting Started: Pendulum Lengths and Periods ......... 12-2 Setting up Statistical Analyses ........................... 12-10 Using the Stat List Editor ................................ 12-11 Attaching Formulas to List Names ....................... 12-14 Detaching Formulas from List Names .................... 12-16 Switching Stat List Editor Contexts ...................... 12-17 Stat List Editor Contexts ................................. 12-18 STAT EDIT Menu ........................................ 12-20 Regression Model Features .............................. 12-22 STAT CALC Menu........................................ 12-24 Statistical Variables ...................................... 12-29 Statistical Analysis in a Program ......................... 12-30 Statistical Plotting ....................................... 12-31 Statistical Plotting in a Program ......................... 12-37 Getting Started: Mean Height of a Population ............ 13-2 Inferential Stat Editors................................... 13-6 STAT TESTS Menu ...................................... 13-9 Inferential Statistics Input Descriptions .................. 13-26 Test and Interval Output Variables ....................... 13-28 Distribution Functions ................................... 13-29 Distribution Shading ..................................... 13-35 Chapter 11: Lists Chapter 12: Statistics Chapter 13: Inferential Statistics and Distributions vi Introduction Chapter 14: Financial Functions Getting Started: Financing a Car ......................... 14-2 Getting Started: Computing Compound Interest.......... 14-3 Using the TVM Solver .................................... 14-4 Using the Financial Functions ........................... 14-5 Calculating Time Value of Money (TVM) ................. 14-6 Calculating Cash Flows .................................. 14-8 Calculating Amortization ................................ 14-9 Calculating Interest Conversion.......................... 14-12 Finding Days between Dates/Defining Payment Method ..... 14-13 Using the TVM Variables ................................. 14-14 Browsing the TI-83 CATALOG ........................... 15-2 Entering and Using Strings ............................... 15-3 Storing Strings to String Variables ....................... 15-4 String Functions and Instructions in the CATALOG ...... 15-6 Hyperbolic Functions in the CATALOG .................. 15-10 Getting Started: Volume of a Cylinder .................... 16-2 Creating and Deleting Programs ......................... 16-4 Entering Command Lines and Executing Programs ...... 16-5 Editing Programs ........................................ 16-6 Copying and Renaming Programs ........................ 16-7 PRGM CTL (Control) Instructions ....................... 16-8 PRGM I/O (Input/Output) Instructions ................... 16-16 Calling Other Programs as Subroutines .................. 16-22 Comparing Test Results Using Box Plots ................ 17-2 Graphing Piecewise Functions ........................... 17-4 Graphing Inequalities .................................... 17-5 Solving a System of Nonlinear Equations ................ 17-6 Using a Program to Create the Sierpinski Triangle ....... 17-7 Graphing Cobweb Attractors ............................ 17-8 Using a Program to Guess the Coefficients ............... 17-9 Graphing the Unit Circle and Trigonometric Curves...... 17-10 Finding the Area between Curves ........................ 17-11 Using Parametric Equations: Ferris Wheel Problem ...... 17-12 Demonstrating the Fundamental Theorem of Calculus ... 17-14 Computing Areas of Regular N-Sided Polygons .......... 17-16 Computing and Graphing Mortgage Payments ........... 17-18 Chapter 15: CATALOG, Strings, Hyperbolic Functions Chapter 16: Programming Chapter 17: Applications Introduction vii Chapter 18: Memory Management Checking Available Memory ............................. Deleting Items from Memory ............................ Clearing Entries and List Elements ...................... Resetting the TI.83 ...................................... 18-2 18-3 18-4 18-5 Chapter 19: Communication Link Getting Started: Sending Variables ....................... 19-2 TI-83 LINK ............................................... 19-3 Selecting Items to Send .................................. 19-4 Receiving Items .......................................... 19-5 Transmitting Items....................................... 19-6 Transmitting Lists to a TI-82 ............................. 19-8 Transmitting from a TI-82 to a TI-83 ..................... 19-9 Backing Up Memory ..................................... 19-10 Table of Functions and Instructions ..................... Menu Map ............................................... Variables ................................................ Statistical Formulas ..................................... Financial Formulas ...................................... A-2 A-39 A-49 A-50 A-54 Appendix A: Tables and Reference Information Appendix B: General Information Battery Information ...................................... B-2 In Case of Difficulty ..................................... B-4 Error Conditions ......................................... B-5 Accuracy Information.................................... B-10 Support and Service Information......................... B-12 Warranty Information .................................... B-13 Index viii Introduction Getting Started: Do This First! Contents TI-83 Keyboard .......................................... TI-83 Menus ............................................. First Steps ............................................... Entering a Calculation: The Quadratic Formula .......... Converting to a Fraction: The Quadratic Formula ........ Displaying Complex Results: The Quadratic Formula .... Defining a Function: Box with Lid ....................... Defining a Table of Values: Box with Lid ................. Zooming In on the Table: Box with Lid ................... Setting the Viewing Window: Box with Lid ............... Displaying and Tracing the Graph: Box with Lid ......... Zooming In on the Graph: Box with Lid .................. Finding the Calculated Maximum: Box with Lid .......... Other TI.83 Features..................................... 2 4 5 6 7 8 9 10 11 12 13 15 16 17 Getting Started 1 TI-83 Keyboard Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. Keyboard Zones Graphing keys access the interactive graphing features. Editing keys allow you to edit expressions and values. Advanced function keys display menus that access the advanced functions. Scientific calculator keys access the capabilities of a standard scientific calculator. Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys 2 Getting Started Using the Color-Coded Keyboard The keys on the TI.83 are color-coded to help you easily locate the key you need. The gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs. The primary function of each key is printed in white on the key. For example, when you press , the MATH menu is displayed. Using the y and Keys The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the TEST menu is displayed. This guidebook describes this keystroke combination as y [TEST]. The alpha function of each key is printed in green above the key. When you press the green key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press and then , the letter A is entered. This guidebook describes this keystroke combination as [A]. The y key accesses the second function printed in yellow above each key. The key accesses the alpha function printed in green above each key. Getting Started 3 TI-83 Menus Displaying a Menu While using your TI.83, you often will need to access items from its menus. When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the MATH menu is displayed as a full screen. After you select an item from a menu, the screen where you are working usually is displayed again. Moving from One Menu to Another Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name. Selecting an Item from a Menu The number or letter next to the current menu item is highlighted. If the menu continues beyond the screen, a down arrow ( $ ) replaces the colon ( : ) in the last displayed item. If you scroll beyond the last displayed item, an up arrow ( # ) replaces the colon in the first item displayed.You can select an item in either of two ways. Press or } to move the cursor to the number or letter of the item; press . Press the key or key combination for the number or letter next to the item. Leaving a Menu without Making a Selection You can leave a menu without making a selection in any of three ways. Press ` to return to the screen where you were. Press y [QUIT] to return to the home screen. Press a key for another menu or screen. 4 Getting Started First Steps Before starting the sample problems in this chapter, follow the steps on this page to reset the TI.83 to its factory settings and clear all memory. This ensures that the keystrokes in this chapter will produce the illustrated results. To reset the TI.83, follow these steps. 1. Press to turn on the calculator. 2. Press and release y, and then press [MEM] (above ). When you press y, you access the operation printed in yellow above the next key that you press. [MEM] is the y operation of the key. The MEMORY menu is displayed. 3. Press 5 to select 5:Reset. The RESET menu is displayed. 4. Press 1 to select 1:All Memory. The RESET MEMORY menu is displayed. 5. Press 2 to select 2:Reset. All memory is cleared, and the calculator is reset to the factory default settings. When you reset the TI.83, the display contrast is reset. If the screen is very light or blank, press and release y, and then press and hold } to darken the screen. If the screen is very dark, press and release y, and then press and hold to lighten the screen. Getting Started 5 Entering a Calculation: The Quadratic Formula Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0 and 2X2 N X + 3 = 0. Begin with the equation 3X2 + 5X + 2 = 0. 1. Press 3 [A] (above ) to store the coefficient of the X2 term. 2. Press [ : ] (above ). The colon allows you to enter more than one instruction on a line. 3. Press 5 [B] (above ) to store the coefficient of the X term. Press [ : ] to enter a new instruction on the same line. Press 2 [C] (above ) to store the constant. 4. Press to store the values to the variables A, B, and C. The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry. 5. Press [B] y [B] 4 [A] [C] 2 [A] to enter the expression for one of the solutions for the quadratic formula, - b + b2 - 4 ac 2a 6. Press to find one solution for the equation 3X2 + 5X + 2 = 0. The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression. 6 Getting Started Converting to a Fraction: The Quadratic Formula You can show the solution as a fraction. 1. Press to display the MATH menu. 2. Press 1 to select 1:4Frac from the MATH menu. When you press 1, Ans4Frac is displayed on the home screen. Ans is a variable that contains the last calculated answer. 3. Press to convert the result to a fraction. To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation. 4. Press y [ENTRY] (above ) to recall the fraction conversion entry, and then press y [ENTRY] again to recall the quadratic-formula expression, - b + b2 - 4 ac 2a 5. Press } to move the cursor onto the + sign in the formula. Press to edit the quadratic-formula expression to become: - b - b2 - 4 ac 2a 6. Press to find the other solution for the quadratic equation 3X2 + 5X + 2 = 0. Getting Started 7 Displaying Complex Results: The Quadratic Formula Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex number mode, the TI.83 displays complex results. 1. Press z (6 times), and then press ~ to position the cursor over a+bi. Press to select a+bi complexnumber mode. 2. Press y [QUIT] (above z) to return to the home screen, and then press ` to clear it. 3. Press 2 [A] [ : ] 1 [B] [ : ] 3 [C] . The coefficient of the X2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively. 4. Press y [ENTRY] to recall the store instruction, and then press y [ENTRY] again to recall the quadratic-formula expression, - b - b2 - 4 ac 2a 5. Press to find one solution for the equation 2X2 N X + 3 = 0. 6. Press y [ENTRY] repeatedly until this quadratic-formula expression is displayed: - b + b2 - 4 ac 2a 7. Press to find the other solution for the quadratic equation: 2X2 N X + 3 = 0. Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver (Chapter 2). 8 Getting Started Defining a Function: Box with Lid Take a 20 cm. 25 cm. sheet of paper and cut X X squares from two corners. Cut X 12.5 cm. rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution. Begin by defining a function that describes the volume of the box. From the diagram: 2X + A = 20 2X + 2B = 25 V=ABX Substituting: V = (20 N 2X) (25 2 N X) X 20 X A X B X 25 B 1. Press o to display the Y= editor, which is where you define functions for tables and graphing. 2. Press 20 2 ,, 25 2 ,, ,, to define the volume function as Y1 in terms of X. ,, lets you enter X quickly, without having to press . The highlighted = sign indicates that Y1 is selected. Getting Started 9 Defining a Table of Values: Box with Lid The table feature of the TI.83 displays numeric information about a function. You can use a table of values from the function defined on page 9 to estimate an answer to the problem. 1. Press y [TBLSET] (above p) to display the TABLE SETUP menu. 2. Press to accept TblStart=0. 3. Press 1 to define the table increment @Tbl=1. Leave Indpnt: Auto and Depend: Auto so that the table will be generated automatically. 4. Press y [TABLE] (above s) to display the table. Notice that the maximum value for Y1 (box's volume) occurs when X is about 4, between 3 and 5. 5. Press and hold to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box's volume) changes from positive to negative, between 10 and 11. 6. Press y [TBLSET]. Notice that TblStart has changed to 6 to reflect the first line of the table as it was last displayed. (In step 5, the first value of X displayed in the table is 6.) 10 Getting Started Zooming In on the Table: Box with Lid You can adjust the way a table is displayed to get more information about a defined function. With smaller values for @Tbl, you can zoom in on the table. 1. Press 3 to set TblStart. Press 1 to set @Tbl. This adjusts the table setup to get a more accurate estimate of X for maximum volume Y1. 2. Press y [TABLE]. 3. Press and } to scroll the table. Notice that the maximum value for Y1 is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6<X<3.8. 4. Press y [TBLSET]. Press 3 6 to set TblStart. Press 01 to set @Tbl. 5. Press y [TABLE], and then press and } to scroll the table. Four equivalent maximum values are shown, 410.60 at X=3.67, 3.68, 3.69, and 3.70. 6. Press and } to move the cursor to 3.67. Press ~ to move the cursor into the Y1 column. The value of Y1 at X=3.67 is displayed on the bottom line in full precision as 410.261226. 7. Press to display the other maximums. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318, and at X=3.7 is 410.256. The maximum volume of the box would occur at 3.68 if you could measure and cut the paper at .01-cm. increments. Getting Started 11 Setting the Viewing Window: Box with Lid You also can use the graphing features of the TI.83 to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window. 1. Press p to display the window editor, where you can view and edit the values of the window variables. The standard window variables define the viewing window as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display. Xscl and Yscl define the distance between tick marks on the X and Y axes. Xres controls resolution. 2. Press 0 to define Xmin. 3. Press 20 2 to define Xmax using an expression. Ymax Xscl Xmax Yscl Ymin Xmin 4. Press . The expression is evaluated, and 10 is stored in Xmax. Press to accept Xscl as 1. 5. Press 0 500 100 1 to define the remaining window variables. 12 Getting Started Displaying and Tracing the Graph: Box with Lid Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the TRACE feature. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(20N2X)(252NX)X is displayed. 2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line. 3. Press |, ~, }, and to move the freemoving cursor to the apparent maximum of the function. As you move the cursor, the X and Y coordinate values are updated continually. Getting Started 13 4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your estimate for the maximum value of X. 6. Press 3 8. When you press a number key while in TRACE, the X= prompt is displayed in the bottom-left corner. 7. Press . The trace cursor jumps to the point on the Y1 function evaluated at X=3.8. 8. Press | and ~ until you are on the maximum Y value. This is the maximum of Y1(X) for the X pixel values. The actual, precise maximum may lie between pixel values. 14 Getting Started Zooming In on the Graph: Box with Lid To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the ZOOM instructions. 1. Press q to display the ZOOM menu. This menu is a typical TI.83 menu. To select an item, you can either press the number or letter next to the item, or you can press until the item number or letter is highlighted, and then press . 2. Press 2 to select 2:Zoom In. The graph is displayed again. The cursor has changed to indicate that you are using a ZOOM instruction. 3. With the cursor near the maximum value of the function (as in step 8 on page 14), press . The new viewing window is displayed. Both XmaxNXmin and YmaxNYmin have been adjusted by factors of 4, the default values for the zoom factors. 4. Press p to display the new window settings. Getting Started 15 Finding the Calculated Maximum: Box with Lid You can use a CALCULATE menu operation to calculate a local maximum of a function. 1. Press y [CALC] (above r) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt. 2. Press | to trace along the curve to a point to the left of the maximum, and then press . A 4 at the top of the screen indicates the selected bound. A Right Bound? prompt is displayed. 3. Press ~ to trace along the curve to a point to the right of the maximum, and then press . A 3 at the top of the screen indicates the selected bound. A Guess? prompt is displayed. 4. Press | to trace to a point near the maximum, and then press . Or, press 3 8, and then press to enter a guess for the maximum. When you press a number key in TRACE, the X= prompt is displayed in the bottomleft corner. Notice how the values for the calculated maximum compare with the maximums found with the free-moving cursor, the trace cursor, and the table. Note: In steps 2 and 3 above, you can enter values directly for Left Bound and Right Bound, in the same way as described in step 4. 16 Getting Started Other TI-83 Features Getting Started has introduced you to basic TI.83 operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI.83. Graphing You can store, graph, and analyze up to 10 functions (Chapter 3), up to six parametric functions (Chapter 4), up to six polar functions (Chapter 5), and up to three sequences (Chapter 6). You can use DRAW operations to annotate graphs (Chapter 8). You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots (Chapter 6). You can create function evaluation tables to analyze many functions simultaneously (Chapter 7). You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously (Chapter 9). You can enter and save up to 10 matrices and perform standard matrix operations on them (Chapter 10). You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves (Chapter 11). You can perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions (Chapter 12). Sequences Tables Split Screen Matrices Lists Statistics Getting Started 17 Inferential Statistics You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically (Chapter 13). You can use time-value-of-money (TVM) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions (Chapter 14). The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI.83. You can paste any function or instruction from the CATALOG to the current cursor location (Chapter 15). You can enter and store programs that include extensive control and input/output instructions (Chapter 16). The TI.83 has a port to connect and communicate with another TI.83, a TI.82, the Calculator-Based Laboratory (CBL 2, CBL) System, a Calculator-Based Ranger (CBR), or a personal computer. The unit-to-unit link cable is included with the TI.83 (Chapter 19). Financial Functions CATALOG Programming Communication Link 18 Getting Started 1 Contents Operating the TI-83 Turning On and Turning Off the TI.83 .................... Setting the Display Contrast ............................. The Display .............................................. Entering Expressions and Instructions ................... TI.83 Edit Keys .......................................... Setting Modes ........................................... Using TI.83 Variable Names ............................. Storing Variable Values .................................. Recalling Variable Values ................................ ENTRY (Last Entry) Storage Area ........................ Ans (Last Answer) Storage Area ......................... TI.83 Menus ............................................. VARS and VARS Y.VARS Menus ......................... Equation Operating System (EOS) ..................... Error Conditions ......................................... 1-2 1-3 1-4 1-6 1-8 1-9 1-13 1-14 1-15 1-16 1-18 1-19 1-21 1-22 1-24 Operating the TI-83 1-1 Turning On and Turning Off the TI-83 Turning On the Calculator To turn on the TI.83, press . If you previously had turned off the calculator by pressing y [OFF], the TI.83 displays the home screen as it was when you last used it and clears any error. If Automatic Power DownTM (APD) had previously turned off the calculator, the TI.83 will return exactly as you left it, including the display, cursor, and any error. To prolong the life of the batteries, APD turns off the TI.83 automatically after about five minutes without any activity. Turning Off the Calculator To turn off the TI.83 manually, press y [OFF]. All settings and memory contents are retained by Constant Memory. Any error condition is cleared. The TI.83 uses four AAA alkaline batteries and has a userreplaceable backup lithium battery (CR1616 or CR1620). To replace batteries without losing any information stored in memory, follow the steps in Appendix B. Batteries 1-2 Operating the TI-83 Setting the Display Contrast Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark. Note: The TI.83 has 40 contrast settings, so each number 0 through 9 represents four settings. The TI.83 retains the contrast setting in memory when it is turned off. To adjust the contrast, follow these steps. 1. Press and release the y key. 2. Press and hold or }, which are below and above the contrast symbol (yellow, half-shaded circle). lightens the screen. } darkens the screen. Note: If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press and release y, and then press and hold } until the display reappears. When to Replace Batteries When the batteries are low, a low-battery message is displayed when you turn on the calculator. To replace the batteries without losing any information in memory, follow the steps in Appendix B. Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI.83 will turn off automatically and the unit will not operate. Batteries must be replaced. All memory is retained. Note: The operating period following the first low-battery message could be longer than two weeks if you use the calculator infrequently. Operating the TI-83 1-3 The Display Types of Displays The TI.83 displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI.83 can display a horizontally or vertically split screen to show graphs and text simultaneously. The home screen is the primary screen of the TI.83. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. When text is displayed, the TI.83 screen can display a maximum of eight lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left. When an entry is executed on the home screen, the answer is displayed on the right side of the next line. Entry Answer Home Screen Displaying Entries and Answers The mode settings control the way the TI.83 interprets expressions and displays answers (page 1.9). If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (...) is displayed to the right or left. Press ~ and | to scroll the answer. Entry Answer Returning to the Home Screen Busy Indicator To return to the home screen from any other screen, press y [QUIT]. When the TI.83 is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line. 1-4 Operating the TI-83 Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character. Cursor Appearance Effect of Next Keystroke Entry Solid rectangle A character is entered at the $ cursor; any existing character is overwritten Underline Insert __ A character is inserted in front of the cursor location Second Reverse arrow A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed Alpha Reverse A An alpha character (green on the keyboard) is entered or SOLVE is executed Full Checkerboard No entry; the maximum characters rectangle are entered at a prompt or memory # is full If you press during an insertion, the cursor becomes an underlined A (A) If you press y during an insertion, the underline cursor becomes an underlined # ( # ). Graphs and editors sometimes display additional cursors, which are described in other chapters. Operating the TI-83 1-5 Entering Expressions and Instructions What Is an Expression? An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI.83, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression. You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value. Entering an Expression To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press , regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS) rules (page 1.22), and the answer is displayed. Most TI.83 functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press 45. Do not enter the letters L, O, and G. If you enter LOG, the TI.83 interprets the entry as implied multiplication of the variables L, O, and G. Calculate 3.76 (L7.9 + 5) + 2 log 45. 3 76 7 9 y 5 2 45 Multiple Entries on a Line To enter two or more expressions or instructions on a line, separate them with colons ( [:]). All instructions are stored together in last entry (ENTRY; page 1.16). 1-6 Operating the TI-83 Entering a Number in Scientific Notation To enter a number in scientific notation, follow these steps. 1. Enter the part of the number that precedes the exponent. This value can be an expression. 2. Press y [EE]. is pasted to the cursor location. 3. If the exponent is negative, press , and then enter the exponent, which can be one or two digits. When you enter a number in scientific notation, the TI.83 does not automatically display answers in scientific or engineering notation. The mode settings (page 1.9) and the size of the number determine the display format. Functions A function returns a value. For example, , L, +, (, and log( are the functions in the example on page 1.6. In general, the first letter of each function is lowercase on the TI.83. Most functions take at least one argument, as indicated by an open parenthesis ( ( ) following the name. For example, sin( requires one argument, sin(value). An instruction initiates an action. For example, ClrDraw is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis ( ( ) at the end of the name. For example, Circle( requires three arguments, Circle(X,Y,radius). To interrupt a calculation or graph in progress, which would be indicated by the busy indicator, press . When you interrupt a calculation, the menu is displayed. To return to the home screen, select 1:Quit. To go to the location of the interruption, select 2:Goto. When you interrupt a graph, a partial graph is displayed. To return to the home screen, press ` or any nongraphing key. To restart graphing, press a graphing key or select a graphing instruction. Instructions Interrupting a Calculation Operating the TI-83 1-7 TI-83 Edit Keys Keystrokes Result ~ or | } or Moves the cursor within an expression; these keys repeat. Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat. On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression. On the bottom line of an expression on the home screen, moves the cursor to the end of the expression. Moves the cursor to the beginning of an expression. Moves the cursor to the end of an expression. Evaluates an expression or executes an instruction. On a line with text on the home screen, clears the current line. On a blank line on the home screen, clears everything on the home screen. In an editor, clears the expression or value where the cursor is located; it does not store a zero. Deletes a character at the cursor; this key repeats. Changes the cursor to __ ; inserts characters in front of the underline cursor; to end insertion, press y [INS] or press |, }, ~, or . Changes the cursor to ; the next keystroke performs a 2nd operation (an operation in yellow above a key and to the left); to cancel 2nd, press y again. Changes the cursor to ; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel , press or press |, }, ~, or . y| y~ ` { y [INS] y y [A.LOCK] Changes the cursor to ; sets alpha-lock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alpha-lock, press ; name prompts set alpha-lock automatically. ,, Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in Seq mode with one keystroke. 1-8 Operating the TI-83 Setting Modes Checking Mode Settings Mode settings control how the TI.83 displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI.83 is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail. Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+bi re^qi Full Horiz G-T Numeric notation Number of decimal places Unit of angle measure Type of graphing Whether to connect graph points Whether to plot simultaneously Real, rectangular cplx, or polar cplx Full screen, two split-screen modes Changing Mode Settings To change mode settings, follow these steps. 1. Press or } to move the cursor to the line of the setting that you want to change. 2. Press ~ or | to move the cursor to the setting you want. 3. Press . Setting a Mode from a Program You can set a mode from a program by entering the name of the mode as an instruction; for example, Func or Float. From a blank command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location. Operating the TI-83 1-9 Normal, Sci, Eng Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format. Normal notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in 12345.67. Sci (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of E, as in 1.234567E4. Eng (engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, as in 12.34567E3. Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI.83 expresses the answer in scientific notation. Float, 0123456789 Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal. 0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press . The decimal setting applies to Normal, Sci, and Eng notation modes. The decimal setting applies to these numbers: An answer displayed on the home screen Coordinates on a graph (Chapters 3, 4, 5, and 6) The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8) Results of CALCULATE operations (Chapters 3, 4, 5, and 6) The regression equation stored after the execution of a regression model (Chapter 12) 1-10 Operating the TI-83 Radian, Degree Angle modes control how the TI.83 interprets angle values in trigonometric functions and polar/rectangular conversions. Radian mode interprets angle values as radians. Answers display in radians. Degree mode interprets angle values as degrees. Answers display in degrees. Func, Par, Pol, Seq Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail. Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3). Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4). Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5). Seq (sequence) graphing mode plots sequences (Chapter 6). Connected, Dot Connected plotting mode draws a line connecting each point calculated for the selected functions. Dot plotting mode plots only the calculated points of the selected functions. Operating the TI-83 1-11 Sequential, Simul Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted. Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X. Note: Regardless of which graphing mode is selected, the TI.83 will sequentially graph all stat plots before it graphs any functions. Real, a+bi, re^qi Real mode does not display complex results unless complex numbers are entered as input. Two complex modes display complex results. a+bi (rectangular complex mode) displays complex numbers in the form a+bi. re^qi (polar complex mode) displays complex numbers in the form re^qi. Full, Horiz, G.T Full screen mode uses the entire screen to display a graph or edit screen. Each split-screen mode displays two screens simultaneously. Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9). G.T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9). 1-12 Operating the TI-83 Using TI-83 Variable Names Variables and Defined Items On the TI.83 you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI.83 uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names. Variable Type Names A, B, . . . , Z, q A, B, . . . , Z, q A, B, C, Real numbers Complex numbers Matrices Lists Functions Parametric equations Polar functions Sequence functions Stat plots Graph databases Graph pictures Strings System variables Notes about Variables . . . , J L1, L2, L3, L4, L5, L6, and user- defined names Y1, Y2, . . . , Y9, Y0 X1T and Y1T, . . . , X6T and Y6T r 1, r 2, r 3, r 4, r 5, r 6 u, v, w Plot1, Plot2, Plot3 GDB1, GDB2, . . . , GDB9, GDB0 Pic1, Pic2, . . . , Pic9, Pic0 Str1, Str2, . . . , Str9, Str0 Xmin, Xmax, and others You can create as many list names as memory will allow (Chapter 11). Programs have user-defined names and share memory with variables (Chapter 16). From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter 15), system variables such as Xmax (Chapter 1), TblStart (Chapter 7), and all Y= functions (Chapters 3, 4, 5, and 6). From an editor, you can store to matrices, lists, and Y= functions (Chapter 3). From the home screen, a program, or an editor, you can store a value to a matrix element or a list element. You can use DRAW STO menu items to store and recall graph databases and pictures (Chapter 8). Operating the TI-83 1-13 Storing Variable Values Storing Values in a Variable Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. To store a value to a variable from the home screen or a program using the key, begin on a blank line and follow these steps. 1. Enter the value you want to store. The value can be an expression. 2. Press . ! is copied to the cursor location. 3. Press and then the letter of the variable to which you want to store the value. 4. Press . If you entered an expression, it is evaluated. The value is stored to the variable. Displaying a Variable Value To display the value of a variable, enter the name on a blank line on the home screen, and then press . 1-14 Operating the TI-83 Recalling Variable Values Using Recall (RCL) To recall and copy variable contents to the current cursor location, follow these steps. To leave RCL, press `. 1. Press y RCL. Rcl and the edit cursor are displayed on the bottom line of the screen. 2. Enter the name of the variable in any of five ways. Press and then the letter of the variable. Press y LIST, and then select the name of the list, or press y [Ln]. Press , and then select the name of the matrix. Press to display the VARS menu or ~ to display the VARS Y.VARS menu; then select the type and then the name of the variable or function. Press |, and then select the name of the program (in the program editor only). The variable name you selected is displayed on the bottom line and the cursor disappears. 3. Press . The variable contents are inserted where the cursor was located before you began these steps. Note: You can edit the characters pasted to the expression without affecting the value in memory. Operating the TI-83 1-15 ENTRY (Last Entry) Storage Area Using ENTRY (Last Entry) When you press on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI.83, ENTRY is retained in memory. To recall ENTRY, press y [ENTRY]. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line. Because the TI.83 updates ENTRY only when you press , you can recall the previous entry even if you have begun to enter the next expression. 57 y [ENTRY] Accessing a Previous Entry The TI.83 retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y [ENTRY] repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area. 1A 2B y [ENTRY] If you press y [ENTRY] after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on. y [ENTRY] 1-16 Operating the TI-83 Reexecuting the Previous Entry After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press . To reexecute the displayed entry, press again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed. 0N N1N : N Multiple Entry Values on a Line To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press . All expressions and instructions separated by colons are stored in ENTRY. When you press y [ENTRY], all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press . For the equation A=pr 2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess. 8R [:] y [p] R y [ENTRY] y | 7 y [INS] 95 Continue until the answer is as accurate as you want. Clearing ENTRY Clear Entries (Chapter 18) clears all data that the TI.83 is holding in the ENTRY storage area. Operating the TI-83 1-17 Ans (Last Answer) Storage Area Using Ans in an Expression When an expression is evaluated successfully from the home screen or from a program, the TI.83 stores the answer to a storage area called Ans (last answer). Ans may be a real or complex number, a list, a matrix, or a string. When you turn off the TI.83, the value in Ans is retained in memory. You can use the variable Ans to represent the last answer in most places. Press y [ANS] to copy the variable name Ans to the cursor location. When the expression is evaluated, the TI.83 uses the value of Ans in the calculation. Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes. 1742 147 y [ANS] Continuing an Expression You can use Ans as the first entry in the next expression without entering the value again or pressing y [ANS]. On a blank line on the home screen, enter the function. The TI.83 pastes the variable name Ans to the screen, then the function. 52 99 Storing Answers To store an answer, store Ans to a variable before you evaluate another expression. Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V. y [p ] 5 33 V 1-18 Operating the TI-83 TI-83 Menus Using a TI-83 Menu You can access most TI.83 operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen. The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted. A number or letter identifies each menu item's place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The LIST NAMES, PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0. When the menu continues beyond the displayed items, a down arrow ( $ ) replaces the colon next to the last displayed item. When a menu item ends in an ellipsis, the item displays a secondary menu or editor when you select it. To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item. Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu. Scrolling a Menu To scroll down the menu items, press . To scroll up the menu items, press }. To page down six menu items at a time, press . To page up six menu items at a time, press }. The green arrows on the calculator, between and }, are the page-down and page-up symbols. To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press . Operating the TI-83 1-19 Selecting an Item from a Menu You can select an item from a menu in either of two ways. Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen. Press or } to move the cursor to the item you want, and then press . After you select an item from a menu, the TI.83 typically displays the previous screen. Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, then the cursor moves beyond it to the next item. Calculate 327. 27 Leaving a Menu without Making a Selection You can leave a menu without making a selection in any of four ways. Press y [QUIT] to return to the home screen. Press ` to return to the previous screen. Press a key or key combination for a different menu, such as or y [LIST]. Press a key or key combination for a different screen, such as o or y [TABLE]. 1-20 Operating the TI-83 VARS and VARS Y-VARS Menus VARS Menu You can enter the names of functions and system variables in an expression or store to them directly. To display the VARS menu, press . All VARS menu items display secondary menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access more than one secondary menu. VARS Y-VARS 1: Window... 2: Zoom... 3: GDB... 4: Picture... 5: Statistics... 6: Table... 7: String... X/Y, T/q, and U/V/W variables ZX/ZY, ZT/Zq, and ZU variables Graph database variables Picture variables XY, G, EQ, TEST, and PTS variables TABLE variables String variables Selecting a Variable from the VARS Menu or VARS Y-VARS Menu To display the VARS Y.VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar display secondary menus of the Y= function variables. VARS Y-VARS 1: Function... 2: Parametric... 3: Polar... 4: On/Off... Yn functions XnT, YnT functions rn functions Lets you select/deselect functions Note: The sequence variables (u, v, w) are located on the keyboard as the second functions of , -, and . To select a variable from the VARS or VARS Y.VARS menu, follow these steps. 1. Display the VARS or VARS Y.VARS menu. Press to display the VARS menu. Press ~ to display the VARS Y.VARS menu. 2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the VARS Y.VARS menu. A secondary menu is displayed. 3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press ~ or | to display other secondary menus. 4. Select a variable name from the menu. It is pasted to the cursor location. Operating the TI-83 1-21 Equation Operating System (EOSTM) Order of Evaluation The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI.83. EOS lets you enter numbers and functions in a simple, straightforward sequence. EOS evaluates the functions in an expression in this order: 1 2 3 4 5 6 7 8 9 Single-argument functions that precede the argument, such as (, sin(, or log( Functions that are entered after the argument, such as 2, M1, !, , r, and conversions Powers and roots, such as 2^5 or 5x32 Permutations (nPr) and combinations (nCr) Multiplication, implied multiplication, and division Addition and subtraction Relational functions, such as > or Logic operator and Logic operators or and xor Within a priority level, EOS evaluates functions from left to right. Calculations within parentheses are evaluated first. Multiargument functions, such as nDeriv(A2,A,6), are evaluated as they are encountered. 1-22 Operating the TI-83 Implied Multiplication The TI.83 recognizes implied multiplication, so you need not press to express multiplication in all cases. For example, the TI.83 interprets 2p, 4sin(46), 5(1+2), and (25)7 as implied multiplication. Note: TI.83 implied multiplication rules differ from those of the TI.82. For example, the TI.83 evaluates 12X as (12)X, while the TI.82 evaluates 12X as 1/(2X) (Chapter 2). Parentheses All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4. You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions. Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the Y= function. Negation To enter a negative number, use the negation key. Press and then enter the number. On the TI.83, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation. For example, MX2, evaluates to a negative number (or 0). Use parentheses to square a negative number. Note: Use the key for subtraction and the key for negation. If you press to enter a negative number, as in 9 7, or if you press to indicate subtraction, as in 9 7, an error occurs. If you press A B, it is interpreted as implied multiplication (AMB). Operating the TI-83 1-23 Error Conditions Diagnosing an Error The TI.83 detects errors while performing these tasks. Evaluating an expression Executing an instruction Plotting a graph Storing a value When the TI.83 detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for the error. If you select 1:Quit (or press y [QUIT] or `), then the home screen is displayed. If you select 2:Goto, then the previous screen is displayed with the cursor at or near the error location. Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program. Correcting an Error To correct an error, follow these steps. 1. Note the error type (ERR:error type). 2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location. 3. Determine the error. If you cannot recognize the error, refer to Appendix B. 4. Correct the expression. 1-24 Operating the TI-83 2 Contents Math, Angle, and Test Operations Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using the Equation Solver ............................... MATH NUM (Number) Operations........................ Entering and Using Complex Numbers................... MATH CPX (Complex) Operations ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ....................................... TEST (Relational) Operations ............................ TEST LOGIC (Boolean) Operations ...................... 2-2 2-3 2-5 2-8 2-13 2-16 2-18 2-20 2-23 2-24 2-26 Math, Angle, and Test Operations 2-1 Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5. 1. Begin on the home screen. Press | to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press . Press 5 to enter the probability of heads. Press . Press 40 to enter the number of simulations. Press . 2. Press to evaluate the expression. A list of 40 elements is displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on. 3. Press y L1 to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram (Chapter 12). 4. Press ~ or | to view the additional counts in the list. Ellipses (...) indicate that the list continues beyond the screen. Note: Since randBin( generates random numbers, your list elements may differ from those in the example. 2-2 Math, Angle, and Test Operations Keyboard Math Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length. + (Addition), N (Subtraction), (Multiplication), (Division) You can use + (addition, ), N (subtraction, ), (multiplication, ), and (division, ) with real and complex numbers, expressions, lists, and matrices. You cannot use with matrices. valueA+valueB valueAvalueB valueA N valueB valueA valueB Trigonometric Functions You can use the trigonometric (trig) functions (sine, ~; cosine, TM; and tangent, s) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example, sin(30) in Radian mode returns L.9880316241; in Degree mode it returns .5. sin(value) cos(value) tan(value) You can use the inverse trig functions (arcsine, y [SINL1]; arccosine, y [COSL1]; and arctangent, y [TANL1]) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. sinL1(value) cosL1(value) tanL1(value) Note: The trig functions do not operate on complex numbers. ^ (Power), 2 (Square), ( (Square Root) You can use ^ (power, >), 2 (square, ), and ( (square root, y ) with real and complex numbers, expressions, lists, and matrices. You cannot use ( with matrices. value^power value2 (value) L1 (Inverse) You can use L1 (inverse, -- ) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1x. valueL1 Math, Angle, and Test Operations 2-3 log(, 10^(, ln( You can use log( (logarithm, ), 10^( (power of 10, y [10x]), and ln( (natural log, ) with real or complex numbers, expressions, and lists. log(value) 10^(power) ln(value) e^( (Exponential) e^( (exponential, y ex]) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. e^(power) e (Constant) e (constant, y [e]) is stored as a constant on the TI-83. Press y [e] to copy e to the cursor location. In calculations, the TI-83 uses 2.718281828459 for e. L (Negation) M (negation, ) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices. Mvalue EOS rules (Chapter 1) determine when negation is evaluated. For example, LA2 returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (LA)2. Note: On the TI-83, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press . p (Pi) p (Pi, y [p]) is stored as a constant in the TI-83. In calculations, the TI-83 uses 3.1415926535898 for p. 2-4 Math, Angle, and Test Operations MATH Operations MATH Menu To display the MATH menu, press . MATH NUM CPX PRB 1: 4Frac Displays the answer as a fraction. 2: 4Dec Displays the answer as a decimal. 3: 3 Calculates the cube. 4: 3( Calculates the cube root. 5: x Calculates the xth root. 6: fMin( Finds the minimum of a function. 7: fMax( Finds the maximum of a function. 8: nDeriv( Computes the numerical derivative. 9: fnInt( Computes the function integral. 0: Solver... Displays the equation solver. 4Frac, 4Dec 4Frac (display as a fraction) displays an answer as its rational equivalent. You can use 4Frac with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4Frac following value. value 4Frac 4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4Dec following value. value 4Dec Math, Angle, and Test Operations 2-5 3(Cube), 3( (Cube Root) 3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices. value3 3( 3( (cube root) returns the cube root of value. You can use with real or complex numbers, expressions, and lists. 3(value) x (Root) x (xth root) returns the xth root of value. You can use x with real or complex numbers, expressions, and lists. xthrootxvalue fMin(, fMax( fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1L5). fMin(expression,variable,lower,upper[,tolerance]) fMax(expression,variable,lower,upper[,tolerance]) Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]). 2-6 Math, Angle, and Test Operations nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1L3). nDeriv( is valid only for real numbers. nDeriv(expression,variable,value[,H]) nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points. f(x) = f(x+H)Nf(xNH) 2H As H becomes smaller, the approximation usually becomes more accurate. You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-83 can return a false derivative value at a nondifferentiable point. fnInt( fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1L5). fnInt( is valid only for real numbers. fnInt(expression,variable,lower,upper[,tolerance]) Tip: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s. Math, Angle, and Test Operations 2-7 Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers. When you select Solver, one of two screens is displayed. The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty. The interactive solver editor (see step 3 picture on page 2.9) is displayed when an equation is stored in eqn. To enter an expression in the equation solver, assuming Entering an Expression in the that the variable eqn is empty, follow these steps. Equation Solver 1. Select 0:Solver from the MATH menu to display the equation editor. 2. Enter the expression in any of three ways. Enter the expression directly into the equation solver. Paste a Y= variable name from the VARS Y.VARS menu to the equation solver. Press y [RCL], paste a Y= variable name from the VARS Y.VARS menu, and press . The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it. 2-8 Math, Angle, and Test Operations 3. Press or . The interactive solver editor is displayed. The equation stored in eqn is set equal to zero and displayed on the top line. Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed. The default lower and upper bounds appear in the last line of the editor (bound={L199,199}). A $ is displayed in the first column of the bottom line if the editor continues beyond the screen. Tip: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor. Entering and Editing Variable Values When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable. You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration. You can store equations to any VARS Y.VARS variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions referenced in the equation. Math, Angle, and Test Operations 2-9 Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press or . 3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-83 will attempt to display the solution that is closest to your guess. The default guess is calculated as (upper + lower) . 2 2-10 Math, Angle, and Test Operations 4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-83 searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L199,199}. 5. Move the cursor to the variable for which you want to solve and press [SOLVE] (above the key). The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen. Note: When a number continues beyond the screen, be sure to press ~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent. The values of the variables are updated in memory. leftNrt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to leftNrt= indicates that the equation has been evaluated at the new value of the variable for which you solved. Math, Angle, and Test Operations 2-11 Editing an Equation Stored to eqn Equations with Multiple Roots To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation. Some equations have more than one solution. You can enter a new initial guess (page 2.10) or new bounds (page 2.11) to look for additional solutions. Further Solutions After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and leftNrt=diff disappear. Move the cursor to the variable for which you now want to solve and press [SOLVE]. Controlling the Solution for Solver or solve( The TI-83 solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions. The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is L199. The default for upper is 199. solve( is valid only for real numbers. solve(expression,variable,guess[,{lower,upper}]) Using solve( on the Home Screen or from a Program expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format. 2-12 Math, Angle, and Test Operations MATH NUM (Number) Operations MATH NUM Menu To display the MATH NUM menu, press ~. MATH NUM CPX PRB 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd( Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor abs( abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices. abs(value) Note: abs( is also available on the MATH CPX menu. round( round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits. round(value[,#decimals]) Math, Angle, and Test Operations 2-13 iPart(, fPart( iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices. iPart(value) fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices. fPart(value) int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers. 2-14 Math, Angle, and Test Operations min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared, min( returns a list of the smaller of each pair of elements. If list and value are compared, min( compares each element in list with value. max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value. min(valueA,valueB) min(list) min(listA,listB) min(list,value) max(valueA,valueB) max(list) max(listA,listB) max(list,value) Note: min( and max( also are available on the LIST MATH menu. lcm(, gcd( lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, lcm( returns a list of the lcm of each pair of elements. If list and value are specified, lcm( finds the lcm of each element in list and value. gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, gcd( returns a list of the gcd of each pair of elements. If list and value are specified, gcd( finds the gcd of each element in list and value. lcm(valueA,valueB) lcm(listA,listB) lcm(list,value) gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) Math, Angle, and Test Operations 2-15 Entering and Using Complex Numbers Complex-Number The TI-83 displays complex numbers in rectangular form and polar form. To select a complex-number mode, press Modes z, and then select either of the two modes. a+bi (rectangular-complex mode) re^qi (polar-complex mode) On the TI-83, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer. Real mode a+bi mode $ $ Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed. Radian mode is recommended for complex number calculations. Internally, the TI-83 converts all entered trig values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions. In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode. Note about Radian versus Degree Mode 2-16 Math, Angle, and Test Operations Interpreting Complex Results Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction (page 2.19). In the example below, re^qi and Radian modes are set. RectangularComplex Mode Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is the real component, b is the imaginary component, and i is a constant equal to -1. To enter a complex number in rectangular form, enter the value of a (real component), press or , enter the value of b (imaginary component), and press y [i] (constant). real component(+ or N)imaginary componenti Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to -1. To enter a complex number in polar form, enter the value of r (magnitude), press y [ ex] (exponential function), enter the value of q (angle), press y [i] (constant), and then press . magnitudee^(anglei) Math, Angle, and Test Operations 2-17 MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( Returns the complex conjugate. 2: real( Returns the real part. 3: imag( Returns the imaginary part. 4: angle( Returns the polar angle. 5: abs( Returns the magnitude (modulus). 6: 4Rect Displays the result in rectangular form. 7: 4Polar Displays the result in polar form. conj( conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers. conj(a+bi) returns aNbi in a+bi mode. conj(re^(qi)) returns re^(Lqi) in re^qi mode. real( real( (real part) returns the real part of a complex number or list of complex numbers. real(a+bi) returns a. real(re^(qi)) returns rcos(q). imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers. imag(a+bi) returns b. imag(re^(qi)) returns rsin(q). 2-18 Math, Angle, and Test Operations angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp<q<p. abs( abs( (absolute value) returns the magnitude (modulus), (real2+imag2) , of a complex number or list of complex numbers. abs(a+bi) returns (a2+b2) . abs(re^(qi)) returns r (magnitude). 4Rect 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Rect returns a+bi. 4Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi). Math, Angle, and Test Operations 2-19 MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |. MATH NUM CPX PRB 1: rand 2: nPr 3: nCr 4: ! 5: randInt( 6: randNorm( 7: randBin( Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution rand rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of randomnumbers, specify an integer > 1 for numtrials (number of trials). The default for numtrials is 1. rand[(numtrials)] Tip: To generate random numbers beyond the range of 0 to 1, you can include rand in an expression. For example, rand5 generates a random number > 0 and < 5. With each rand execution, the TI-83 generates the same random-number sequence for a given seed value. The TI-83 factory-set seed value for rand is 0. To generate a different random-number sequence, store any nonzero seed value to rand. To restore the factory-set seed value, store 0 to rand or reset the defaults (Chapter 18). Note: The seed value also affects randInt(, randNorm(, and randBin( instructions (page 2.22). 2-20 Math, Angle, and Test Operations nPr, nCr nPr (number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nPr number nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nCr number ! (Factorial) ! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ,L.5 and 69. value! Note: The factorial is computed recursively using the relationship (n+1)! = nn!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L12)!=p is used to complete the calculation. Hence: n!=n(nN1)(nN2) ... 21, if n is an integer ,0 n!= n(nN1)(nN2) ... 12p, if n+12 is an integer ,0 n! is an error, if neither n nor n+12 is an integer ,0. (The variable n equals value in the syntax description above.) Math, Angle, and Test Operations 2-21 randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1. randInt(lower,upper[,numtrials]) randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1. randNorm(m,s[,numtrials]) randBin( randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be , 1. prob (probability of success) must be , 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions (page 2-20). 2-22 Math, Angle, and Test Operations ANGLE Operations ANGLE Menu To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-83's interpretation of ANGLE menu entries. ANGLE 1: 2: ' 3: r 4: 8DMS 5: R8Pr( 6: R8Pq( 7: P8Rx( 8: P8Ry( Degree notation DMS minute notation Radian notation Displays as degree/minute/second Returns r, given X and Y Returns q, given X and Y Returns x, given R and q Returns y, given R and q DMS Entry Notation DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (), the minute symbol ('), and the second symbol ("). degrees must be a real number; minutes and seconds must be real numbers , 0. degreesminutes'seconds" For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use so that the TI-83 can interpret the argument as degrees, minutes, and seconds. Degree mode Radian mode (Degree) (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use to convert degrees to radians. value {value1,value2,value3,value4,...,value n} also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format. Note: " is not on the ANGLE menu. To enter ", press . Math, Angle, and Test Operations 2-23 r (Radians) r (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees. valuer Degree mode 8DMS 8DMS (degree/minute/second) displays answer in DMS format (page 2.23). The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line. answer8DMS R8Pr (, R8Pq ( , P8Rx(, P8Ry( R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists. R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set. 2-24 Math, Angle, and Test Operations TEST (Relational) Operations TEST Menu To display the TEST menu, press y [TEST]. This operator... TEST LOGIC 1: = 2: 3: > 4: , 5: < 6: Returns 1 (true) if... Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to =, , >, ,, <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists. For = and only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are matrices, both must have the same dimensions. Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values. valueA=valueB valueA>valueB valueA<valueB valueAvalueB valueA,valueB valueAvalueB Using Tests Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1). The expression 2+2=2+3 returns 0. The TI-83 performs the addition first because of EOS rules, and then it compares 4 to 5. The expression 2+(2=2)+3 returns 6. The TI-83 performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3. Math, Angle, and Test Operations 2-25 TEST LOGIC (Boolean) Operations TEST LOGIC Menu To display the TEST LOGIC menu, press y TEST ~. This operator... TEST LOGIC 1: and 2: or 3: xor 4: not( Returns a 1 (true) if... Both values are nonzero (true). At least one value is nonzero (true). Only one value is zero (false). The value is zero (false). Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true). and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists. and, or, xor valueA and valueB valueA or valueB valueA xor valueB valueA valueB and or 1 1 1 0 xor 0 1 1 0 0 0 0 0 not( 0 0 0 0 returns returns returns returns 1 0 0 0 not( returns 1 if value (which can be an expression) is 0. not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C. 2-26 Math, Angle, and Test Operations 3 Contents Function Graphing Getting Started: Graphing a Circle ....................... Defining Graphs ......................................... Setting the Graph Modes ................................. Defining Functions ...................................... Selecting and Deselecting Functions ..................... Setting Graph Styles for Functions ....................... Setting the Viewing Window Variables ................... Setting the Graph Format ................................ Displaying Graphs ....................................... Exploring Graphs with the Free-Moving Cursor .......... Exploring Graphs with TRACE ........................... Exploring Graphs with the ZOOM Instructions ........... Using ZOOM MEMORY .................................. Using the CALC (Calculate) Operations .................. 3-2 3-3 3-4 3-5 3-7 3-9 3-11 3-13 3-15 3-17 3-18 3-20 3-23 3-25 Function Graphing 3-1 Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle. 1. In Func mode, press o to display the Y= editor. Press y 100 ,, to enter the expression Y=(100NX 2), which defines the top half of the circle. The expression Y=L(100NX 2) defines the bottom half of the circle. On the TI-83, you can define one function in terms of another. To define Y2=LY1, press to enter the negation sign. Press ~ to display the VARS Y.VARS menu. Then press to select 1:Function. The FUNCTION secondary menu is displayed. Press 1 to select 1:Y1. 2. Press q 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s. Notice that the functions appear as an ellipse in the standard viewing window. 3. To adjust the display so that each pixel represents an equal width and height, press q 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display. 4. To see the ZSquare window variables, press p and notice the new values for Xmin, Xmax, Ymin, and Ymax. 3-2 Function Graphing Defining Graphs TI-83--Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing. To define a graph in any graphing mode, follow these steps. Some steps are not always necessary. 1. Press z and set the appropriate graph mode (page 3.4). 2. Press o and enter, edit, or select one or more functions in the Y= editor (page 3.5 and 3.7). 3. Deselect stat plots, if necessary (page 3.7). 4. Set the graph style for each function (page 3.9). 5. Press p and define the viewing window variables (page 3.11). 6. Press y [FORMAT] and select the graph format settings (page 3.13). Defining a Graph Displaying and Exploring a Graph Saving a Graph for Later Use After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI-83 tools described in this chapter. You can store the elements that define the current graph to any of 10 graph database variables (GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph. These types of information are stored in a GDB. Y= functions Graph style settings Window settings Format settings You can store a picture of the current graph display to any of 10 graph picture variables (Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph. Function Graphing 3-3 Setting the Graph Modes Checking and Changing the Graphing Mode To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select Func mode before you enter values for the window variables and before you enter the functions. The TI-83 has four graphing modes. Func (function graphing) Par (parametric graphing; Chapter 4) Pol (polar graphing; Chapter 5) Seq (sequence graphing; Chapter 6) Other mode settings affect graphing results. Chapter 1 describes each mode setting. Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates. Radian or Degree angle mode affects interpretation of some functions. Connected or Dot plotting mode affects plotting of selected functions. Sequential or Simul graphing-order mode affects function plotting when more than one function is selected. Setting Modes from a Program To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps. 1. Press z to display the mode settings. 2. Press , ~, |, and } to place the cursor on the mode that you want to select. 3. Press to paste the mode name to the cursor location. The mode is changed when the program is executed. 3-4 Function Graphing Defining Functions Displaying Functions in the Y= Editor To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected. Defining or Editing a Function To define or edit a function, follow these steps. 1. Press o to display the Y= editor. 2. Press to move the cursor to the function you want to define or edit. To erase a function, press `. 3. Enter or edit the expression to define the function. You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned. The independent variable in the function is X. Func mode defines ,, as X. To enter X, press ,, or press [X]. When you enter the first character, the = is highlighted, indicating that the function is selected. As you enter the expression, it is stored to the variable Yn as a user-defined function in the Y= editor. 4. Press or to move the cursor to the next function. Function Graphing 3-5 Defining a Function from the Home Screen or a Program To define a function from the home screen or a program, begin on a blank line and follow these steps. 1. Press , enter the expression, and then press again. 2. Press . 3. Press ~ 1 to select 1:Function from the VARS Y.VARS menu. 4. Select the function name, which pastes the name to the cursor location on the home screen or program editor. 5. Press to complete the instruction. "expression"!Yn When the instruction is executed, the TI-83 stores the expression to the designated variable Yn, selects the function, and displays the message Done. Evaluating Y= Functions in Expressions You can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list. Yn(value) Yn({value1,value2,value3, . . .,value n}) 3-6 Function Graphing Selecting and Deselecting Functions Selecting and Deselecting a Function You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-83 graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0. To select or deselect a function in the Y= editor, follow these steps. 1. Press o to display the Y= editor. 2. Move the cursor to the function you want to select or deselect. 3. Press | to place the cursor on the function's = sign. 4. Press to change the selection status. When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected. Turning On or Turning Off a Stat Plot in the Y= Editor To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line. To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor on Plot1, Plot2, or Plot3, and then press . Plot1 is turned on. Plot2 and Plot3 are turned off. Function Graphing 3-7 Selecting and Deselecting Functions from the Home Screen or a Program To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps. 1. Press ~ to display the VARS Y.VARS menu. 2. Select 4:On/Off to display the ON/OFF secondary menu. 3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location. 4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off. If you enter two or more numbers, separate them with commas. To turn on or turn off all functions, do not enter a number after FnOn or FnOff. FnOn[function#,function#, . . .,function n] FnOff[function#,function#, . . .,function n] 5. Press . When the instruction is executed, the status of each function in the current mode is set and Done is displayed. For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turns on Y1 and Y3. 3-8 Function Graphing Setting Graph Styles for Functions Graph Style Icons in the Y= Editor This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line. Icon Style Description Line Thick Above Below Path A solid line connects plotted points; this is the default in Connected mode A thick solid line connects plotted points Shading covers the area a*bove the graph Shading covers the area below the graph A circular cursor traces the leading edge of the graph and draws a path Animate A circular cursor traces the leading edge of the graph without drawing a path Dot A small dot represents each plotted point; this is the default in Dot mode Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes. Setting the Graph To set the graph style for a function, follow these steps. Style 1. Press o to display the Y= editor. 2. Press and } to move the cursor to the function. 3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.) 4. Press repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above. 5. Press ~, }, or when you have selected a style. Function Graphing 3-9 Shading Above and Below When you select or for two or more functions, the TI-83 rotates through four shading patterns. Vertical lines shade the first function with a or graph style. Horizontal lines shade the second. Negatively sloping diagonal lines shade the third. Positively sloping diagonal lines shade the fourth. The rotation returns to vertical lines for the fifth or function, repeating the order described above. When shaded areas intersect, the patterns overlap. Note: When or is selected for a Y= function that graphs a family of curves, such as Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves. Setting a Graph Style from a Program To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graph style, as shown below. 1 = (line) 4 = (below) 2 = (thick) 5 = (path) 7 = (dot) 3 = (above) 6= (animate) GraphStyle(function#,graphstyle#) For example, when this program is executed in Func mode, GraphStyle(1,3) sets Y1 to (above). 3-10 Function Graphing Setting the Viewing Window Variables The TI-83 Viewing The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) Window defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0. Ymax Xscl Xmax Yscl Ymin Xmin Displaying the Window Variables To display the current window variable values, press p. The window editor above and to the right shows the default values in Func graphing mode and Radian angle mode. The window variables differ from one graphing mode to another. Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1. At Xres=1, functions are evaluated and graphed at each pixel on the x-axis. At Xres=8, functions are evaluated and graphed at every eighth pixel along the x-axis. Tip: Small Xres values improve graph resolution but may cause the TI-83 to draw graphs more slowly. Changing a Window Variable Value To change a window variable value from the window editor, follow these steps. 1. Press or } to move the cursor to the window variable you want to change. 2. Edit the value, which can be an expression. Enter a new value, which clears the original value. Move the cursor to a specific digit, and then edit it. 3. Press , , or }. If you entered an expression, the TI-83 evaluates it. The new value is stored. Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph. Function Graphing 3-11 Storing to a Window Variable from the Home Screen or a Program To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps. 1. Enter the value you want to store. 2. Press . 3. Press to display the VARS menu. 4. Select 1:Window to display the Func window variables (X/Y secondary menu). Press ~ to display the Par and Pol window variables (T/q secondary menu). Press ~ ~ to display the Seq window variables (U/V/W secondary menu). 5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location. 6. Press to complete the instruction. When the instruction is executed, the TI-83 stores the value to the window variable and displays the value. @X and @Y The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy). @X and @Y are calculated from Xmin, Xmax, Ymin, and Ymax when you display a graph. @X = (Xmax N Xmin) 94 @Y = (Ymax N Ymin) 62 You can store values to @X and @Y. If you do, Xmax and Ymax are calculated from @X, Xmin, @Y, and Ymin. 3-12 Function Graphing Setting the Graph Format Displaying the Format Settings To display the format settings, press y [FORMAT]. The default settings are highlighted below. RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff Sets cursor coordinates. Sets coordinates display on or off. Sets grid off or on. Sets axes on or off. Sets axes label off or on. Sets expression display on or off. Format settings define a graph's appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6). Changing a Format Setting To change a format setting, follow these steps. 1. Press , ~, }, and | as necessary to move the cursor to the setting you want to select. 2. Press to select the highlighted setting. RectGC, PolarGC RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y. PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q. The RectGC/PolarGC setting determines which variables are updated when you plot the graph, move the freemoving cursor, or trace. RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed. PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q are displayed. Function Graphing 3-13 CoordOn, CoordOff CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff format is selected, the function number is displayed in the top-right corner. CoordOff (coordinates off) does not display the function number or coordinates. GridOff, GridOn Grid points cover the viewing window in rows that correspond to the tick marks (page 3.11) on each axis. GridOff does not display grid points. GridOn displays grid points. AxesOn, AxesOff AxesOn displays the axes. AxesOff does not display the axes. This overrides the LabelOff/ LabelOn format setting. LabelOff, LabelOn ExprOn, ExprOff LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected. ExprOn and ExprOff determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots. When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen. When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced. 3-14 Function Graphing Displaying Graphs Displaying a New Graph To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-83 plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. While plotting a graph, you can pause or stop graphing. Pausing or Stopping a Graph Press to pause; then press to resume. Press to stop; then press s to redraw. Smart Graph Smart Graph is a TI-83 feature that redisplays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed. If you performed any of these actions since the graph was last displayed, the TI-83 will replot the graph based on new values when you press s. Changed a mode setting that affects graphs Changed a function in the current picture Selected or deselected a function or stat plot Changed the value of a variable in a selected function Changed a window variable or graph format setting Cleared drawings by selecting ClrDraw Changed a stat plot definition Function Graphing 3-15 Overlaying Functions on a Graph On the TI-83, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press s. Then store cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function. Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-83 plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on. {2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X). {2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X). Note: When using more than one list, the lists must have the same dimensions. 3-16 Function Graphing Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or , the cursor moves from the center of the viewing window. As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal mode setting determines the number of decimal digits displayed for the coordinate values. To display the graph with no cursor and no coordinate values, press ` or . When you press |, ~, }, or , the cursor moves from the same position. Graphing Accuracy The free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r (page 3.18). The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a ZoomIn) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates. Free-moving cursor "on" the curve Function Graphing 3-17 Exploring Graphs with TRACE Beginning a Trace Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected. The Y= expression is displayed in the top-left corner of the screen, if ExprOn format is selected. To move the TRACE cursor . . . do this: Moving the Trace Cursor . . . to the previous or next plotted point, . . . five plotted points on a function (Xres affects this), press | or ~. press y | or y ~. . . . to any valid X value on a function, enter a value, and then press . . . . from one function to another, press } or . When the trace cursor moves along a function, the Y value is calculated from the X value; that is, Y=Yn(X). If the function is undefined at an X value, the Y value is blank. Trace cursor on the curve If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Moving the Trace Cursor from Function to Function To move the trace cursor from function to function, press and }. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If ExprOn format is selected, the expression is updated. 3-18 Function Graphing Moving the Trace Cursor to Any Valid X Value To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an X= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor. Note: This feature does not apply to stat plots. Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window. While tracing, you can press to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in TRACE. When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph (page 3.15). On a blank line in the program editor, press r. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press to resume program execution. Quick Zoom Leaving and Returning to TRACE Using TRACE in a Program Function Graphing 3-19 Exploring Graphs with the ZOOM Instructions ZOOM Menu To display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs. ZOOM MEMORY 1: ZBox 2: Zoom In 3: Zoom Out 4: ZDecimal 5: ZSquare 6: ZStandard 7: ZTrig 8: ZInteger 9: ZoomStat 0: ZoomFit Draws a box to define the viewing window. Magnifies the graph around the cursor. Views more of a graph around the cursor. Sets @X and @Y to 0.1. Sets equal-size pixels on the X and Y axes. Sets the standard window variables. Sets the built-in trig window variables. Sets integer values on the X and Y axes. Sets the values for current stat lists. Fits YMin and YMax between XMin and XMax. Zoom Cursor When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+). To define a new viewing window using ZBox, follow these steps. 1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of the screen. 2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press . When you move the cursor away from the first defined corner, a small, square dot indicates the spot. 3. Press |, }, ~, or . As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen. Note: To cancel ZBox before you press , press `. ZBox 4. When you have defined the box, press to replot the graph. To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press `. 3-20 Function Graphing Zoom In, Zoom Out Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom. To zoom in on a graph, follow these steps. 1. Check XFact and YFact (page 3.24); change as needed. 2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed. 3. Move the zoom cursor to the point that is to be the center of the new viewing window. 4. Press . The TI-83 adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location. 5. Zoom in on the graph again in either of two ways. To zoom in at the same point, press . To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press . To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5. To cancel Zoom In or Zoom Out, press `. ZDecimal ZDecimal replots the functions immediately. It updates the window variables to preset values, as shown below. These values set @X and @Y equal to 0.1 and set the X and Y value of each pixel to one decimal place. Xmin=L4.7 Xmax=4.7 Xscl=1 Ymin=L3.1 Ymax=3.1 Yscl=1 ZSquare ZSquare replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that @X=@Y, which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph. Function Graphing 3-21 ZStandard ZStandard replots the functions immediately. It updates the window variables to the standard values shown below. Xmin=L10 Xmax=10 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 Xres=1 ZTrig ZTrig replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below. Xmin=L(4724)p Xmax=(4724)p Xscl=p/2 Ymin=L4 Ymax=4 Yscl=1 ZInteger ZInteger redefines the viewing window to the dimensions shown below. To use ZInteger, move the cursor to the point that you want to be the center of the new window, and then press ; ZInteger replots the functions. @X=1 @Y=1 Xscl=10 Yscl=10 ZoomStat ZoomStat redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only Xmin and Xmax are adjusted. ZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to include the minimum and maximum Y values of the selected functions between the current XMin and XMax. XMin and XMax are not changed. ZoomFit 3-22 Function Graphing Using ZOOM MEMORY ZOOM MEMORY Menu To display the ZOOM MEMORY menu, press q ~. ZOOM MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors... Uses the previous viewing window. Stores the user-defined window. Recalls the user-defined window. Changes Zoom In and Zoom Out factors. ZPrevious ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. ZoomSto ZoomSto immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined ZOOM variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres. These variables apply to all graphing modes. For example, changing the value of ZXmin in Func mode also changes it in Par mode. ZoomRcl ZoomRcl graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the ZoomSto instruction. The window variables are updated with the user-defined values, and the graph is plotted. Function Graphing 3-23 ZOOM FACTORS The zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around a point. To display the ZOOM FACTORS screen, where you can review the current values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown are the defaults. Checking XFact and YFact Changing XFact and YFact You can change XFact and YFact in either of two ways. Enter a new value. The original value is cleared automatically when you enter the first digit. Place the cursor on the digit you want to change, and then enter a value or press { to delete it. From the home screen or a program, you can store directly to any of the user-defined ZOOM variables. Using ZOOM MEMORY Menu Items from the Home Screen or a Program From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM MEMORY menu. 3-24 Function Graphing Using the CALC (Calculate) Operations CALCULATE Menu To display the CALCULATE menu, press y CALC. Use the items on this menu to analyze the current graph functions. CALCULATE 1: value 2: zero 3: minimum 4: maximum 5: intersect 6: dy/dx 7: f(x)dx Calculates a function Y value for a given X. Finds a zero (x-intercept) of a function. Finds a minimum of a function. Finds a maximum of a function. Finds an intersection of two functions. Finds a numeric derivative of a function. Finds a numeric integral of a function. value value evaluates one or more currently selected functions for a specified value of X. Note: When a value is displayed for X, press ` to clear the value. When no value is displayed, press ` to cancel the value operation. To evaluate a selected function at X, follow these steps. 1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner. 2. Enter a real value, which can be an expression, for X between Xmin and Xmax. 3. Press . The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if CoordOff format is selected. To move the cursor from function to function at the entered X value, press } or . To restore the free-moving cursor, press | or ~. Function Graphing 3-25 zero zero finds a zero (x-intercept or root) of a function using solve(. Functions can have more than one x-intercept value; zero finds the zero closest to your guess. The time zero spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess. To find a zero of a function, follow these steps. 1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner. 2. Press } or to move the cursor onto the function for which you want to find a zero. 3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press . A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press | or ~ (or enter a value) to select the x-value for the right bound, and then press . A 3 indicator on the graph screen shows the right bound. Guess? is then displayed in the bottom-left corner. 4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press . The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~. 3-26 Function Graphing minimum, maximum minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1L5. To find a minimum or maximum, follow these steps. 1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed. 2. Select the function and set left bound, right bound, and guess as described for zero (steps 2 through 4; page 3.26). The cursor is on the solution, and the coordinates are displayed, even if you have selected CoordOff format; Minimum or Maximum is displayed in the bottom-left corner. To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~. intersect intersect finds the coordinates of a point at which two or more functions intersect using solve(. The intersection must appear on the display to use intersect. To find an intersection, follow these steps. 1. Select 5:intersect from the CALCULATE menu. The current graph is displayed with First curve? in the bottom-left corner. 2. Press or }, if necessary, to move the cursor to the first function, and then press . Second curve? is displayed in the bottom-left corner. 3. Press or }, if necessary, to move the cursor to the second function, and then press . 4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press . The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner. To restore the freemoving cursor, press |, }, ~, or . Function Graphing 3-27 dy/dx dy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point, with H=1L3. To find a function's slope at a point, follow these steps. 1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed. 2. Press } or to select the function for which you want to find the numerical derivative. 3. Press | or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press . The cursor is on the solution and the numerical derivative is displayed. To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~. f(x)dx f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It uses the fnInt( function, with a tolerance of H=1L3. To find the numerical derivative of a function, follow these steps. 1. Select 7:f(x)dx from the CALCULATE menu. The current graph is displayed with Lower Limit? in the bottom-left corner. 2. Press } or to move the cursor to the function for which you want to calculate the integral. 3. Set lower and upper limits as you would set left and right bounds for zero (step 3; page 3.26). The integral value is displayed, and the integrated area is shaded. Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area. 3-28 Function Graphing 4 Contents Parametric Graphing Getting Started: Path of a Ball ........................... Defining and Displaying Parametric Graphs .............. Exploring Parametric Graphs ............................ 4-2 4-4 4-7 Parametric Graphing 4-1 Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity. For initial velocity v 0 and angle q, the position of the ball as a function of time has horizontal and vertical components. Horizontal: Vertical: X1(t)=tv 0cos(q) 1 Y1(t)=tv 0sin(q)N 2 gt2 Y2(t)=Y1(t) Y3(t)=0 The vertical and horizontal vectors of the ball's motion also will be graphed. Vertical vector: X2(t)=0 Horizontal vector: X3(t)=X1(t) Gravity constant: g=9.8 m/sec2 1. Press z. Press ~ to select Par mode. Press ~ to select Simul for simultaneous graphing of all three parametric equations in this example. 2. Press o. Press 30 ,, TM 25 y [ANGLE] 1 (to select ) to define X1T in terms of T. 3. Press 30 ,, ~ 25 y [ANGLE] 1 9.8 2 ,, to define Y1T. The vertical component vector is defined by X2T and Y2T. 4. Press 0 to define X2T. 5. Press ~ to display the VARS Y.VARS menu. Press 2 to display the PARAMETRIC secondary menu. Press 2 to define Y2T. 4-2 Parametric Graphing The horizontal component vector is defined by X3T and Y3T. 6. Press ~ 2, and then press 1 to define X3T. Press 0 to define Y3T. 7. Press | | } to change the graph style to for X3T and Y3T. Press } to change the graph style to for X2T and Y2T. Press } to change the graph style to for X1T and Y1T. (These keystrokes assume that all graph styles were set to originally.) 8. Press p. Enter these values for the window variables. Tmin=0 Tmax=5 Tstep=.1 Xmin=L10 Xmax=100 Xscl=50 Ymin=L5 Ymax=15 Yscl=10 9. Press y [FORMAT] ~ to set AxesOff, which turns off the axes. 10. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion. Tip: To simulate the ball flying through the air, set graph style to (animate) for X1T and Y1T. 11. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for X (distance), Y (height), and T (time) are displayed at the bottom of the screen. Parametric Graphing 4-3 Defining and Displaying Parametric Graphs TI-83 Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing. To display the mode screen, press z. To graph parametric equations, you must select Par graphing mode before you enter window variables and before you enter the components of parametric equations. After selecting Par graphing mode, press o to display the parametric Y= editor. Setting Parametric Graphing Mode Displaying the Parametric Y= Editor In this editor, you can display and enter both the X and Y components of up to six equations, X1T and Y1T through X6T and Y6T. Each is defined in terms of the independent variable T. A common application of parametric graphs is graphing equations over time. Selecting a Graph Style The icons to the left of X1T through X6T represent the graph style of each parametric equation (Chapter 3). The default in Par mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for parametric graphing. 4-4 Parametric Graphing Defining and Editing Parametric Equations To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In Par graphing mode, you can enter the parametric variable T in either of two ways. Press ,,. Press T. Two components, X and Y, define a single parametric equation. You must define both of them. Selecting and Deselecting Parametric Equations The TI-83 graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the = signs of both the X and Y components are highlighted. You may select any or all of the equations X1T and Y1T through X6T and Y6T. To change the selection status, move the cursor onto the = sign of either the X or Y component and press . The status of both the X and Y components is changed. Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Par graphing in Radian angle mode. Tmin=0 Tmax=6.2831853... Tstep=.1308996... Xmin=L10 Xmax=10 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 Smallest T value to evaluate Largest T value to evaluate (2p) T value increment (p24) Smallest X value to be displayed Largest X value to be displayed Spacing between the X tick marks Smallest Y value to be displayed Largest Y value to be displayed Spacing between the Y tick marks Note: To ensure that sufficient points are plotted, you may want to change the T window variables. Parametric Graphing 4-5 Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting. Displaying a Graph When you press s, the TI-83 plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y. The window variables define the viewing window. As the graph is plotted, X, Y, and T are updated. Smart Graph applies to parametric graphs (Chapter 3). Window Variables and Y-VARS Menus You can perform these actions from the home screen or a program. Access functions by using the name of the X or Y component of the equation as a variable. Store parametric equations. Select or deselect parametric equations. Store values directly to window variables. 4-6 Parametric Graphing Exploring Parametric Graphs Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one Tstep at a time. When you begin a trace, the trace cursor is on the first selected function at Tmin. If ExprOn is selected, then the function is displayed. In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on. In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T. To move five plotted points at a time on a function, press y | or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Quick Zoom is available in Par graphing; panning is not (Chapter 3). Parametric Graphing 4-7 Moving the Trace Cursor to Any Valid T Value To move the trace cursor to any valid T value on the current function, enter the number. When you enter the first digit, a T= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the T= prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor. ZOOM ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par graphing. CALC CALC operations in Par graphing work the same as in Func graphing. The CALCULATE menu items available in Par graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt. 4-8 Parametric Graphing 5 Contents Polar Graphing Getting Started: Polar Rose .............................. Defining and Displaying Polar Graphs ................... Exploring Polar Graphs .................................. 5-2 5-3 5-6 Polar Graphing 5-1 Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1. Press z to display the mode screen. Press ~ ~ to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings. 2. Press o to display the polar Y= editor. Press 8 ~ 2.5 ,, to define r 1. 3. Press q 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets qmax=2p and defines the window, rather than the pixels, as square. 4. Press p to display the window variables. Press 4 y [p] to increase the value of qmax to 4p. 5. Press q 5 to select 5:ZSquare and plot the graph. 6. Repeat steps 2 through 5 with new values for the variables A and B in the polar equation r1=Asin(Bq). Observe how the new values affect the graph. 5-2 Polar Graphing Defining and Displaying Polar Graphs TI-83 Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing. To display the mode screen, press z. To graph polar equations, you must select Pol graphing mode before you enter values for the window variables and before you enter polar equations. After selecting Pol graphing mode, press o to display the polar Y= editor. Setting Polar Graphing Mode Displaying the Polar Y= Editor In this editor, you can enter and display up to six polar equations, r1 through r6. Each is defined in terms of the independent variable q (page 5.4). Selecting Graph Styles The icons to the left of r1 through r6 represent the graph style of each polar equation (Chapter 3). The default in Pol graphing mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for polar graphing. Polar Graphing 5-3 Defining and Editing Polar Equations To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways. Press ,,. Press q. The TI-83 graphs only the selected polar equations. In the Selecting and Deselecting Polar Y= editor, a polar equation is selected when the = sign is highlighted. You may select any or all of the equations. Equations To change the selection status, move the cursor onto the = sign, and then press . Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode. qmin=0 qmax=6.2831853... qstep=.1308996... Xmin=L10 Xmax=10 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 Smallest q value to evaluate Largest q value to evaluate (2p) Increment between q values (p24) Smallest X value to be displayed Largest X value to be displayed Spacing between the X tick marks Smallest Y value to be displayed Largest Y value to be displayed Spacing between the Y tick marks Note: To ensure that sufficient points are plotted, you may want to change the q window variables. 5-4 Polar Graphing Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings. Displaying a Graph When you press s, the TI-83 plots the selected polar equations. It evaluates R for each value of q (from qmin to qmax in intervals of qstep) and then plots each point. The window variables define the viewing window. As the graph is plotted, X, Y, R, and q are updated. Smart Graph applies to polar graphs (Chapter 3). Window Variables and Y.VARS Menus You can perform these actions from the home screen or a program. Access functions by using the name of the equation as a variable. Store polar equations. Select or deselect polar equations. Store values directly to window variables. Polar Graphing 5-5 Exploring Polar Graphs Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time. When you begin a trace, the trace cursor is on the first selected function at qmin. If ExprOn format is selected, then the equation is displayed. In RectGC format, TRACE updates the values of X, Y, and q; if CoordOn format is selected, X, Y, and q are displayed. In PolarGC format, TRACE updates X, Y, R, and q; if CoordOn format is selected, R and q are displayed. To move five plotted points at a time on a function, press y | or y ~. If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Quick Zoom is available in Pol graphing mode; panning is not (Chapter 3). TRACE Moving the Trace Cursor to Any Valid q Value To move the trace cursor to any valid q value on the current function, enter the number. When you enter the first digit, a q= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the q= prompt. The value must be valid for the current viewing window. When you complete the entry, press to move the cursor. ZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. ZOOM The q window variables (qmin, qmax, and qstep) are not affected, except when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and 6:Zqstep are zoom memory variables for Pol graphing. CALC CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq. 5-6 Polar Graphing 6 Contents Sequence Graphing Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes Combinations ............................ Exploring Sequence Graphs.............................. Graphing Web Plots...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI.82 Sequence Variables .......... Keystroke Differences Between TI-83 and TI-82 ......... 6-2 6-3 6-8 6-9 6-11 6-12 6-13 6-15 6-16 Sequence Graphing 6-1 Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees? 1. Press z. Press ~ ~ ~ to select Seq graphing mode. 2. Press y [FORMAT] and select Time axes format and ExprOn format if necessary. 3. Press o. If the graph-style icon is not (dot), press | |, press until is displayed, and then press ~ ~. 4. Press ~ 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press 8 y [u] ,, 1 to define the number of trees after each harvest. Press 1000 to define the new trees. Press 4000 to define the number of trees at the beginning of the program. 5. Press p 0 to set nMin=0. Press 50 to set nMax=50. nMin and nMax evaluate forest size over 50 years. Set the other window variables. PlotStart=1 PlotStep=1 Xmin=0 Xmax=50 Xscl=10 Ymin=0 Ymax=6000 Yscl=1000 6. Press r. Tracing begins at nMin (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees? 6-2 Sequence Graphing Defining and Displaying Sequence Graphs TI-83 Graphing Mode Similarities The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing. Setting Sequence To display the mode screen, press z. To graph sequence functions, you must select Seq graphing mode Graphing Mode before you enter window variables and before you enter sequence functions. Sequence graphs automatically plot in Simul mode, regardless of the current plotting-order mode setting. TI-83 Sequence Functions u, v, and w The TI-83 has three sequence functions that you can enter from the keyboard: u, v, and w. They are above the , -, and keys. You can define sequence functions in terms of: The independent variable n The previous term in the sequence function, such as u(nN1) The term that precedes the previous term in the sequence function, such as u(nN2) The previous term or the term that precedes the previous term in another sequence function, such as u(nN1) or u(nN2) referenced in the sequence v(n). Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2). Sequence Graphing 6-3 Displaying the Sequence Y= Editor After selecting Seq mode, press o to display the sequence Y= editor. In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit the value for nMin, which is the sequence window variable that defines the minimum n value to evaluate. The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively. nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin in one editor, the new value for nMin is updated in both editors. Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value. Selecting Graph Styles The icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence (Chapter 3). The default in Seq mode is (dot), which shows discrete values. Dot, (line), and (thick) styles are available for sequence graphing. Graph styles are ignored in Web format. The TI-83 graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the = signs of both u(n)= and u(nMin)= are highlighted. To change the selection status of a sequence function, move the cursor onto the = sign of the function name, and then press . The status is changed for both the sequence function u(n) and its initial value u(nMin). Selecting and Deselecting Sequence Functions 6-4 Sequence Graphing Defining and Editing a Sequence Function To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is n. In Seq graphing mode, you can enter the sequence variable in either of two ways. Press ,,. Press y [CATALOG] [N]. You can enter the function name from the keyboard. To enter the function name u, press y [u] (above ). To enter the function name v, press y [v] (above -). To enter the function name w, press y [w] (above ). Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. n is always a series of consecutive integers, starting at zero or any positive integer. Nonrecursive Sequences In a nonrecursive sequence, the nth term is a function of the independent variable n. Each term is independent of all other terms. For example, in the nonrecursive sequence below, you can calculate u(5) directly, without first calculating u(1) or any previous term. The sequence equation above returns the sequence 2, 4, 6, 8, 10, . . . for n = 1, 2, 3, 4, 5, . . . . Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences. Sequence Graphing 6-5 Recursive Sequences In a recursive sequence, the nth term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by u(nN1) and u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n. For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4). Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, . . . Tip: On the TI-83, you must type each character of the terms. For example, to enter u(nN1), press y [u] ,, . Recursive sequences require an initial value or values, since they reference undefined terms. If each term in the sequence is defined in relation to the previous term, as in u(nN1), you must specify an initial value for the first term. If each term in the sequence is defined in relation to the term that precedes the previous term, as in u(nN2), you must specify initial values for the first two terms. Enter the initial values as a list enclosed in braces ({ }) with commas separating the values. The value of the first term is 0 and the value of the second term is 1 for the sequence u(n). 6-6 Sequence Graphing Setting Window Variables To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes. nMin=1 nMax=10 PlotStart=1 PlotStep=1 Xmin=L10 Xmax=10 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 Smallest n value to evaluate Largest n value to evaluate First term number to be plotted Incremental n value (for graphing only) Smallest X value to be displayed Largest X value to be displayed Spacing between the X tick marks Smallest Y value to be displayed Largest Y value to be displayed Spacing between the Y tick marks nMin must be an integer , 0. nMax, PlotStart, and PlotStep must be integers , 1. nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor. nMax is the largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1), u(nMin+2) , . . . , u(nMax). PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set PlotStart=5. The first four terms are evaluated but are not plotted on the graph. PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify PlotStep=2, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer. Sequence Graphing 6-7 Selecting Axes Combinations Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode. Time Web uv vw uw RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff Type of sequence plot (axes) Rectangular or polar output Cursor coordinate display on/off Grid display off or on Axes display on or off Axes label display off or on Expression display on or off Setting Axes Format For sequence graphing, you can select from five axes formats. The table below shows the values that are plotted on the x-axis and y-axis for each axes setting. Axes Setting Time Web uv vw uw x-axis n u(nN1), v(nN1), w(nN1) u(n) v(n) u(n) y-axis u(n), v(n), w(n) u(n), v(n), w(n) v(n) w(n) w(n) See pages 6.11 and 6.12 for more information on Web plots. See page 6.13 for more information on phase plots (uv, vw, and uw axes settings). Displaying a Sequence Graph To plot the selected sequence functions, press s. As a graph is plotted, the TI-83 updates X, Y, and n. Smart Graph applies to sequence graphs (Chapter 3). 6-8 Sequence Graphing Exploring Sequence Graphs Free-Moving Cursor The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. The axes format setting affects TRACE. When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time. To move five plotted points at once, press y ~ or y |. When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window. Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press . The trace cursor returns to nMin. In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function. Tip: To move the cursor to a specified n during a trace, enter a value for n, and press . For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press . TRACE Moving the Trace Cursor to Any Valid n Value To move the trace cursor to any valid n value on the current function, enter the number. When you enter the first digit, an n = prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the n = prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor. Sequence Graphing 6-9 ZOOM ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing. CALC The only CALC operation available in Seq graphing is value. When Time axes format is selected, value displays Y (the u(n) value) for a specified n value. When Web axes format is selected, value draws the web and displays Y (the u(n) value) for a specified n value. When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n). Evaluating u, v, and w To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can evaluate these names in any of three ways. Calculate the nth value in a sequence. Calculate a list of values in a sequence. Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1. 6-10 Sequence Graphing Graphing Web Plots Graphing a Web Plot To select Web axes format, press y [FORMAT] ~ . A web plot graphs u(n) versus u(nN1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes. When Web axes format is selected, a sequence will not graph properly or will generate an error. It must be recursive with only one recursion level (u(nN1) but not u(nN2)). It cannot reference n directly. It cannot reference any defined sequence except itself. Valid Functions for Web Plots Displaying the Graph Screen In Web format, press s to display the graph screen. The TI-83: Draws a y=x reference line in AxesOn format. Plots the selected sequences with u(nN1) as the independent variable. Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence's initial value. Drawing the Web To activate the trace cursor, press r. The screen displays the sequence and the current n, X, and Y values (X represents u(nN1) and Y represents u(n)). Press ~ repeatedly to draw the web step by step, starting at nMin. In Web format, the trace cursor follows this course. 1. It starts on the x-axis at the initial value u(nMin) (when PlotStart=1). 2. It moves vertically (up or down) to the sequence. 3. It moves horizontally to the y=x reference line. 4. It repeats this vertical and horizontal movement as you continue to press ~. Sequence Graphing 6-11 Using Web Plots to Illustrate Convergence Example: Convergence 1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to (dot), and then define nMin, u(n) and u(nMin) as shown below. 2. Press y [FORMAT] to set Time axes format. 3. Press p and set the variables as shown below. nMin=1 nMax=25 PlotStart=1 PlotStep=1 Xmin=0 Xmax=25 Xscl=1 Ymin=L10 Ymax=10 Ysclhapter for details. Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1. Press z to set Func graphing mode. 2. Press o. Press ,, 3 to select 3. Then press 2 ,, to enter the function Y1=X3N2X. 3. Press y [TBLSET] to display the TABLE SETUP screen. Press 10 to set TblStart=L10. Press 1 to set @Tbl=1. Press to select Indpnt: Auto (automatically generated independent values). Press to select Depend: Auto (automatically generated dependent values). 4. Press y [TABLE] to display the table screen. 5. Press until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values? 7-2 Tables Setting Up the Table TABLE SETUP Screen To display the TABLE SETUP screen, press y [TBLSET]. TblStart, @Tbl TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected). @Tbl (table step) defines the increment for the independent variable. Note: In Seq mode, both TblStart and @Tbl must be integers. Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask Selections Indpnt: Auto Depend: Auto Indpnt: Ask Depend: Auto Table Characteristics Values are displayed automatically in both the independent-variable column and in all dependent-variable columns. The table is empty; when you enter a value for the independent variable, all corresponding dependent-variable values are calculated and displayed automatically. Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press . The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press . Indpnt: Auto Depend: Ask Indpnt: Ask Depend: Ask Setting Up the Table from the Home Screen or a Program To store a value to TblStart, @Tbl, or TblZnput from the home screen or a program, select the variable name from the VARS TABLE secondary menu. TblZnput is a list of independent-variable values in the current table. When you press y [TBLSET] in the program editor, you can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk. Tables 7-3 Defining the Dependent Variables Defining Dependent Variables from the Y= Editor In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In Par mode, you must define both components of each parametric equation (Chapter 4). To edit a selected Y= function from the table editor, follow these steps. 1. Press y [TABLE] to display the table, then press ~ or | to move the cursor to a dependent-variable column. 2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line. Editing Dependent Variables from the Table Editor 3. Press . The cursor moves to the bottom line. Edit the function. 4. Press or . The new values are calculated. The table and the Y= function are updated automatically. Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table. 7-4 Tables Displaying the Table The Table To display the table, press y [TABLE]. Current cell Independentvariable values in the first column Dependentvariable values in the second and third columns Current cell's full value Note: The table abbreviates the values, if necessary. Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable X and the dependent variables Y1 and Y2 are displayed because Func graphing mode is set. Graphing Mode Func (function) Par (parametric) Pol (polar) Seq (sequence) Independent Variable X T q n Dependent Variable Y1 through Y9, and Y0 X1T/Y1T through X6T/Y6T r1 through r6 u(n), v(n), and w(n) Clearing the Table from the Home Screen or a Program From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press . From a program, select 9:ClrTable from the PRGM I/O menu or from the CATALOG. The table is cleared upon execution. If IndpntAsk is selected, all independent and dependent variable values on the table are cleared. If DependAsk is selected, all dependent variable values on the table are cleared. Tables 7-5 Scrolling IndependentVariable Values If Indpnt: Auto is selected, you can press } and in the independent-variable column to display more values. As you scroll the column, the corresponding dependentvariable values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected. Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and @Tbl=1 generates and displays values of X=0, . . . , 6; but you can press } to scroll back and display the table for X=M1, . . ., 5. Displaying Other Dependent Variables If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially. Press ~ or | to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with Par graphing mode and G.T split-screen mode set. Tip: To simultaneously display on the table two dependent variables that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6. 7-6 Tables 8 Contents Draw Instructions Getting Started: Drawing a Tangent Line ................. Using the DRAW Menu ................................... Clearing Drawings ....................................... Drawing Line Segments .................................. Drawing Horizontal and Vertical Lines ................... Drawing Tangent Lines .................................. Drawing Functions and Inverses ......................... Shading Areas on a Graph ............................... Drawing Circles.......................................... Placing Text on a Graph ................................. Using Pen to Draw on a Graph ........................... Drawing Points on a Graph .............................. Drawing Pixels .......................................... Storing Graph Pictures (Pics) ............................ Recalling Graph Pictures (Pics) .......................... Storing Graph Databases (GDBs) ........................ Recalling Graph Databases (GDBs) ...................... 8-2 8-3 8-4 8-5 8-6 8-8 8-9 8-10 8-11 8-12 8-13 8-14 8-16 8-17 8-18 8-19 8-20 DRAW Instructions 8-1 Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to find the equation of the tangent line at X = 2/2 for the function Y = sinX. Before you begin, select Radian and Func mode from the mode screen, if necessary. 1. Press o to display the Y= editor. Press ~ ,, to store sin(X) in Y1. 2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window. 3. Press y [DRAW] 5 to select 5:Tangent(. The tangent instruction is initiated. 4. Press y 2 2. 5. Press . The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. 8-2 DRAW Instructions Using the DRAW Menu DRAW Menu To display the DRAW menu, press y [DRAW]. The TI-83's interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: ClrDraw Clears all drawn elements. 2: Line( Draws a line segment between 2 points. 3: Horizontal Draws a horizontal line. 4: Vertical Draws a vertical line. 5: Tangent( Draws a line segment tangent to a function. 6: DrawF Draws a function. 7: Shade( Shades an area between two functions. 8: DrawInv Draws the inverse of a function. 9: Circle( Draws a circle. 0: Text( Draws text on a graph screen. A: Pen Activates the free-form drawing tool. Before Drawing on a Graph The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions. Change the mode settings on the mode screen. Change the format settings on the format screen. Enter or edit functions in the Y= editor. Select or deselect functions in the Y= editor. Change the window variable values. Turn stat plots on or off. Clear existing drawings with ClrDraw (page 8.4). Note: If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again. Drawing on a Graph You can use any DRAW menu instructions except DrawInv to draw on Func, Par, Pol, and Seq graphs. DrawInv is valid only in Func graphing. The coordinates for all DRAW instructions are the display's x-coordinate and y-coordinate values. You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a DRAW menu instruction, the home screen is displayed. DRAW Instructions 8-3 Clearing Drawings Clearing Drawings When a Graph Is Displayed All points, lines, and shading drawn on a graph with DRAW instructions are temporary. To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements. To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select 1:ClrDraw from the DRAW menu. The instruction is copied to the cursor location. Press . When ClrDraw is executed, it clears all drawings from the current graph and displays the message Done. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone. Clearing Drawings from the Home Screen or a Program Note: Before you clear drawings, you can store them with StorePic (page 8.17). 8-4 DRAW Instructions Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select 2:Line( from the DRAW menu. 2. Place the cursor on the point where you want the line segment to begin, and then press . 3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press . To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press `. Drawing a Line Segment from the Home Screen or a Program Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions. Line(X1,Y1,X2,Y2) To erase a line segment, enter Line(X1,Y1,X2,Y2,0) DRAW Instructions 8-5 Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor. 2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass. 3. Press to draw the line on the graph. To continue drawing lines, repeat steps 2 and 3. To cancel Horizontal or Vertical, press `. 8-6 DRAW Instructions Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list. Horizontal y Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list. Vertical x To instruct the TI-83 to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ). DRAW Instructions 8-7 Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps. 1. Select 5:Tangent( from the DRAW menu. 2. Press and } to move the cursor to the function for which you want to draw the tangent line. The current graph's Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line. 4. Press . In Func mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the dy/dx value is displayed. Tip: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression. expression is interpreted as being in Func mode. Tangent(expression,value) 8-8 DRAW Instructions Drawing Functions and Inverses Drawing a Function DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-83 returns to the home screen or the program editor. DrawF is not interactive. DrawF expression Note: You cannot use a list in expression to draw a family of curves. Drawing an Inverse of a Function DrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis. When you select 8:DrawInv from the DRAW menu, the TI-83 returns to the home screen or the program editor. DrawInv is not interactive. DrawInv works in Func mode only. DrawInv expression Note: You cannot use a list in expression to draw a family of curves. DRAW Instructions 8-9 Shading Areas on a Graph Shading a Graph To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded. Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between Xmin and Xmax, which are the defaults. pattern specifies one of four shading patterns. pattern=1 pattern=2 pattern=3 pattern=4 vertical (default) horizontal negative--slope 45 positive--slope 45 patres specifies one of eight shading resolutions. patres=1 patres=2 patres=3 patres=4 patres=5 patres=6 patres=7 patres=8 shades every pixel (default) shades every second pixel shades every third pixel shades every fourth pixel shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres]) 8-10 DRAW Instructions Drawing Circles Drawing a Circle Directly on a Graph To draw a circle directly on a displayed graph using the cursor, follow these steps. 1. Select 9:Circle( from the DRAW menu. 2. Place the cursor at the center of the circle you want to draw. Press . 3. Move the cursor to a point on the circumference. Press to draw the circle on the graph. Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the Circle( instruction from the home screen or a program, the current window variables may distort the shape. To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press `. Drawing a Circle from the Home Screen or a Program Circle( draws a circle with center (X,Y ) and radius. These values can be expressions. Circle(X,Y,radius) Tip: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular. DRAW Instructions 8-11 Placing Text on a Graph Placing Text Directly on a Graph To place text on a graph when the graph is displayed, follow these steps. 1. Select 0:Text( from the DRAW menu. 2. Place the cursor where you want the text to begin. 3. Enter the characters. Press or y [A.LOCK] to enter letters and q. You may enter TI-83 functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph. To cancel Text(, press `. Placing Text on a Graph from the Home Screen or a Program Text( places on the current graph the characters comprising value, which can include TI-83 functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions. Text(row,column,value,value . . .) value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-83 will evaluate an expression and display the result with up to 10 characters. Split Screen On a Horiz split screen, the maximum value for row is 25. On a G.T split screen, the maximum value for row is 45, and the maximum value for column is 46. 8-12 DRAW Instructions Using Pen to Draw on a Graph Using Pen to Draw on a Graph Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. To draw on a displayed graph, follow these steps. 1. Select A:Pen from the DRAW menu. 2. Place the cursor on the point where you want to begin drawing. Press to turn on the pen. 3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time. 4. Press to turn off the pen. For example, Pen was used to create the arrow pointing to the local minimum of the selected function. To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel Pen, press `. DRAW Instructions 8-13 Drawing Points on a Graph DRAW POINTS Menu To display the DRAW POINTS menu, press y [DRAW] ~. The TI-83's interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: Pt-On( Turns on a point. 2: Pt-Off( Turns off a point. 3: Pt-Change( Toggles a point on or off. 4: Pxl-On( Turns on a pixel. 5: Pxl-Off( Turns off a pixel. 6: Pxl-Change( Toggles a pixel on or off. 7: pxl-Test( Returns 1 if pixel on, 0 if pixel off. Drawing Points Directly on a Graph with Pt-On( To draw a point on a graph, follow these steps. 1. Select 1:Pt.On( from the DRAW POINTS menu. 2. Move the cursor to the position where you want to draw the point. 3. Press to draw the point. To continue drawing points, repeat steps 2 and 3. To cancel Pt.On(, press `. 8-14 DRAW Instructions Erasing Points with Pt-Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select 2:Pt.Off( (point off) from the DRAW POINTS menu. 2. Move the cursor to the point you want to erase. 3. Press to erase the point. To continue erasing points, repeat steps 2 and 3. To cancel Pt.Off(, press `. Changing Points with Pt-Change( To change (toggle on or off) a point on a graph, follow these steps. 1. Select 3:Pt.Change( (point change) from the DRAW POINTS menu. 2. Move the cursor to the point you want to change. 3. Press to change the point's on/off status. To continue changing points, repeat steps 2 and 3. To cancel Pt.Change(, press `. Drawing Points from the Home Screen or a Program Pt.On( (point on) turns on the point at (X=x,Y=y). Pt.Off( turns the point off. Pt.Change( toggles the point on or off. mark is optional; it determines the point's appearance; specify 1, 2, or 3, where: 1 = (dot; default) Pt.On(x,y[,mark]) Pt.Off(x,y[,mark]) Pt.Change(x,y) 2 = > (box) 3 = + (cross) Note: If you specified mark to turn on a point with Pt.On(, you must specify mark when you turn off the point with Pt.Off(. Pt.Change( does not have the mark option. DRAW Instructions 8-15 Drawing Pixels TI-83 Pixels A pixel is a square dot on the TI-83 display. The Pxl. (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-83 returns to the home screen or the program editor. The pixel instructions are not interactive. Turning On and Off Pixels with Pxl-On( and Pxl-Off( Pxl.On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and 62 and column is an integer between 0 and 94. Pxl.Off( turns the pixel off. Pxl.Change( toggles the pixel on and off. Pxl.On(row,column) Pxl.Off(row,column) Pxl.Change(row,column) Using pxl-Test( pxl.Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94. pxl.Test(row,column) Split Screen On a Horiz split screen, the maximum value for row is 30 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(. On a G.T split screen, the maximum value for row is 50 and the maximum value for column is 46 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(. 8-16 DRAW Instructions Storing Graph Pictures (Pics) DRAW STO Menu To display the DRAW STO menu, press y [DRAW] |. When you select an instruction from the DRAW STO menu, the TI-83 returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecallGDB Stores the current picture. Recalls a saved picture. Stores the current graph database. Recalls a saved graph database. Storing a Graph Picture You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program. A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture. To store a graph picture, follow these steps. 1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-83 will store the picture to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to StorePic. 3. Press to display the current graph and store the picture. DRAW Instructions 8-17 Recalling Graph Pictures (Pics) Recalling a Graph Picture To recall a graph picture, follow these steps. 1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-83 will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic. 3. Press to display the current graph with the picture superimposed on it. Note: Pictures are drawings. You cannot trace a curve that is part of a picture. Deleting a Graph Picture To delete graph pictures from memory, use the MEMORY DELETE FROM menu (Chapter 18). 8-18 DRAW Instructions Storing Graph Databases (GDBs) What Is a Graph Database? A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs. A GDB stores five elements of a graph. Graphing mode Window variables Format settings All functions in the Y= editor and the selection status of each Graph style for each Y= function GDBs do not contain drawn items or stat plot definitions. Storing a Graph Database To store a graph database, follow these steps. 1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-83 will store the GDB to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to StoreGDB. 3. Press to store the current database to the specified GDB variable. DRAW Instructions 8-19 Recalling Graph Databases (GDBs) Recalling a Graph Database CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB. To recall a graph database, follow these steps. 1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB. For example, if you enter 7, the TI-83 will recall the GDB stored to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to RecallGDB. 3. Press to replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-83 changes the graphing mode automatically, if necessary. Deleting a Graph Database To delete a GDB from memory, use the MEMORY DELETE FROM menu (Chapter 18). 8-20 DRAW Instructions 9 Contents Split Screen Getting Started: Exploring the Unit Circle................ Using Split Screen ....................................... Horiz (Horizontal) Split Screen .......................... G.T (Graph-Table) Split Screen .......................... TI-83 Pixels in Horiz and G.T Mode ...................... 9-2 9-3 9-4 9-5 9-6 Split Screen 9-1 Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. Use G.T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0, 30, 45, 60, 90, and so on. 1. Press z to display the mode screen. Press ~ to select Degree mode. Press ~ to select Par (parametric) graphing mode. Press ~ ~ to select G.T (graph-table) split-screen mode. 2. Press y [FORMAT] to display the format screen. Press ~ to select ExprOff. 3. Press o to display the Y= editor for Par graphing mode. Press TM ,, to store cos(T) to X1T. Press ~ ,, to store sin(T) to Y1T. 4. Press p to display the window editor. Enter these values for the window variables. Tmin=0 Tmax=360 Tstep=15 Xmin=L2.3 Xmax=2.3 Xscl=1 Ymin=L2.5 Ymax=2.5 Yscl=1 5. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of X1T (cos(T)) is 1 and Y1T (sin(T)) is 0. Press ~ to move the cursor to the next 15 angle increment. As you trace around the circle in steps of 15, an approximation of the standard value for each angle is highlighted in the table. 9-2 Split Screen Using Split Screen Setting a SplitScreen Mode To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen. Select Horiz (horizontal) to display the graph screen and another screen split horizontally. Select G.T (graph-table) to display the graph screen and table screen split vertically. $ $ The split screen is activated when you press any key that applies to either half of the split screen. Some screens are never displayed as split screens. For example, if you press z in Horiz or G.T mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns. When you press a key or key combination in either Horiz or G.T mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed. If you press y [TABLE], the cursor is placed in the half in which the table is displayed. The TI-83 will remain in split-screen mode until you change back to Full screen mode. Split Screen 9-3 Horiz (Horizontal) Split Screen Horiz Mode In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors. Moving from Half to Half in Horiz Mode Home screen (four lines) Y= editor (four lines) Stat list editor (two rows) Window editor (three settings) Table editor (two rows) To use the top half of the split screen: Press s or r. Select a ZOOM or CALC operation. To use the bottom half of the split screen: Press any key or key combination that displays the home screen. Press o (Y= editor). Press ... (stat list editor). Press p (window editor). Press y [TABLE] (table editor). Full Screens in Horiz Mode All other screens are displayed as full screens in Horiz split-screen mode. To return to the Horiz split screen from a full screen when in Horiz mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor. 9-4 Split Screen G-T (Graph-Table) Split Screen G-T Mode In G.T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves. The left half displays the graph. The right half displays the table. Moving from Half to Half in G-T Mode To use the left half of the split screen: Press s or r. Select a ZOOM or CALC operation. To use the right half of the split screen, press y [TABLE]. Using r in G-T Mode As you move the trace cursor along a graph in the split screen's left half in G.T mode, the table on the right half automatically scrolls to match the current cursor values. Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph. Full Screens in G.T Mode All screens other than the graph and the table are displayed as full screens in G.T split-screen mode. To return to the G.T split screen from a full screen when in G.T mode, press any key or key combination that displays the graph or the table. Split Screen 9-5 TI-83 Pixels in Horiz and G-T Modes TI-83 Pixels in Horiz and G-T Modes Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. DRAW POINTS Menu Pixel Instructions For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(: In Horiz mode, row must be {30; column must be {94. In G.T mode, row must be {50; column must be {46. Pxl.On(row,column) DRAW Menu Text( Instruction For the Text( instruction: In Horiz mode, row must be {25; column must be {94. In G.T mode, row must be {45; column must be {46. Text(row,column,"text") PRGM I/O Menu Output( Instruction For the Output( instruction: In Horiz mode, row must be {4; column must be {16. In G.T mode, row must be {8; column must be {16. Output(row,column,"text") Setting a Split-Screen Mode from the Home Screen or a Program To set Horiz or G.T from a program, follow these steps. 1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G.T. The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution. Note: You also can paste Horiz or G.T to the home screen or program editor from the CATALOG (Chapter 15). 9-6 Split Screen 10 Contents Matrices Getting Started: Systems of Linear Equations ............ 10-2 Defining a Matrix ........................................ 10-2 Viewing and Editing Matrix Elements .................... 10-4 Using Matrices with Expressions ........................ 10-7 Displaying and Copying Matrices ........................ 10-8 Using Math Functions with Matrices ..................... 10-9 Using the MATRX MATH Operations ..................... 10-12 Matrices 10-1 Getting Started: Systems of Linear Equations Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A] 2. Press 2 4 to define a 24 matrix. The rectangular cursor indicates the current element. Ellipses (...) indicate additional columns beyond the screen. 3. Press 1 to enter the first element. The rectangular cursor moves to the second column of the first row. 4. Press 2 3 3 to complete the first row for X + 2Y + 3Z = 3. 5. Press 2 3 4 3 to enter the second row for 2X + 3Y + 4Z = 3. 6. Press y [QUIT] to return to the home screen. If necessary, press ` to clear the home screen. Press ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen. 7. Press 1 to select 1: [A] from the MATRX NAMES menu. Press . The reduced row-echelon form of the matrix is displayed and stored in Ans. 1X N 1Z = L3 1Y + 2Z = 3 so X = L3 + Z so Y = 3 N 2Z 10-2 Matrices Defining a Matrix What Is a Matrix? A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-83 has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-83 matrices. Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps. 1. Press | to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed. Selecting a Matrix 2. Select the matrix you want to define. The MATRX EDIT screen is displayed. Accepting or Changing Matrix Dimensions The dimensions of the matrix (row column) are displayed on the top line. The dimensions of a new matrix are 1 1. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension. To accept the row dimension, press . To change the row dimension, enter the number of rows (up to 99), and then press . The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press , the rectangular cursor moves to the first matrix element. Matrices 10-3 Viewing and Editing Matrix Elements Displaying Matrix Elements After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line. This is an 8 4 matrix. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Deleting a Matrix To delete matrices from memory, use the MEMORY DELETE FROM secondary menu (Chapter 18). 10-4 Matrices Viewing a Matrix The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions. Viewing-Context Keys Key Function | or ~ or } Moves the rectangular cursor within the current row. Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension. Switches to editing context; activates the edit cursor on the bottom line. Switches to editing context; clears the value on the bottom line. Switches to editing context; clears the value on the bottom line; copies the character to the bottom line. Nothing Nothing ` Any entry character y [INS] { Matrices 10-5 Editing a Matrix Element In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps. 1. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions. 2. Press |, }, ~, and to move the cursor to the matrix element you want to change. 3. Switch to editing context by pressing , `, or an entry key. 4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context. Note: You can press ` to restore the value at the rectangular cursor if you make a mistake. 5. Press , }, or to move to another element. Editing-Context Keys Key Function | or ~ or } Moves the edit cursor within the value. Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column. Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element. Clears the value on the bottom line. Copies the character to the location of the edit cursor on the bottom line. Activates the insert cursor. Deletes the character under the edit cursor on the bottom line. ` Any entry character y [INS] { 10-6 Matrices Using Matrices with Expressions Using a Matrix in an Expression To use a matrix in an expression, you can do any of the following. Copy the name from the MATRX NAMES menu. Recall the contents of the matrix into the expression with y [RCL] (Chapter 1). Enter the matrix directly (see below). Entering a Matrix in an Expression You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression. To enter a matrix in an expression, follow these steps. 1. Press y [ [ ] to indicate the beginning of the matrix. 2. Press y [ [ ] to indicate the beginning of a row. 3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas. 4. Press y [ ] ] to indicate the end of a row. 5. Repeat steps 2 through 4 to enter all of the rows. 6. Press y [ ] ] to indicate the end of the matrix. Note: The closing ]] are not necessary at the end of an expression or preceding !. The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]] Any expressions are evaluated when the entry is executed. Note: The commas that you must enter to separate elements are not displayed on output. Matrices 10-7 Displaying and Copying Matrices Displaying a Matrix To display the contents of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press . Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Press ~, |, , and } to scroll the matrix. Copying One Matrix to Another To copy a matrix, follow these steps. 1. Press to display the MATRX NAMES menu. 2. Select the name of the matrix you want to copy. 3. Press . 4. Press again and select the name of the new matrix to which you want to copy the existing matrix. 5. Press to copy the matrix to the new matrix name. Accessing a Matrix Element On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES menu. [matrix](row,column) 10-8 Matrices Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-83 keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same. To add () or subtract () matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements. matrixA+matrixB matrixANmatrixB To multiply () two matrices together, the column dimension of matrixA must match the row dimension of matrixB. matrixAmatrixB + (Add), (Subtract), (Multiply) Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value. matrixvalue valuematrix L (Negation) Negating a matrix () returns a matrix in which the sign of every element is changed (reversed). Lmatrix Matrices 10-9 abs( abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs(matrix) round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits. round(matrix[,#decimals]) M1 (Inverse) Use the L1 function (-- ) to invert a matrix (^L1 is not valid). matrix must be square. The determinant cannot equal zero. matrix L1 Powers To raise a matrix to a power, matrix must be square. You can use 2 (), 3 (MATH menu), or ^power (>) for integer power between 0 and 255. matrix 2 matrix 3 matrix ^power 10-10 Matrices Relational Operations To compare two matrices using the relational operations = and (TEST menu), they must have the same dimensions. = and compare matrixA and matrixB on an element-byelement basis. The other relational operations are not valid with matrices. matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is false. matrixAmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false. iPart(, fPart(, int( iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu. iPart( returns a matrix containing the integer part of each element of matrix. fPart( returns a matrix containing the fractional part of each element of matrix. int( returns a matrix containing the greatest integer of each element of matrix. iPart(matrix) fPart(matrix) int(matrix) Matrices 10-11 Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press ~. NAMES MATH EDIT 1: det( Calculates the determinant. 2: T Transposes the matrix. 3: dim( Returns the matrix dimensions. 4: Fill( Fills all elements with a constant. 5: identity( Returns the identity matrix. 6: randM( Returns a random matrix. 7: augment( Appends two matrices. 8: Matr4list( Stores a matrix to a list. 9: List4matr( Stores a list to a matrix. 0: cumSum( Returns the cumulative sums of a matrix. A: ref( Returns the row-echelon form of a matrix. B: rref( Returns the reduced row-echelon form. C: rowSwap( Swaps two rows of a matrix. D: row+( Adds two rows; stores in the second row. E: row( Multiplies the row by a number. F: row+( Multiplies the row, adds to the second row. det( det( (determinant) returns the determinant (a real number) of a square matrix. det(matrix) T (Transpose) T (transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix. matrixT Accessing Matrix Dimensions with dim( dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix. dim(matrix) Note: dim(matrix)!Ln:Ln(1) returns the number of rows. dim(matrix)!Ln:Ln(2) returns the number of columns. 10-12 Matrices Creating a Matrix with dim( Use dim( with to create a new matrixname of dimensions rows columns with 0 as each element. {rows,columns}!dim(matrixname) Redimensioning a Matrix with dim( Use dim( with to redimension an existing matrixname to dimensions rows columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted. {rows,columns}!dim(matrixname) Fill( Fill( stores value to every element in matrixname. Fill(value,matrixname) identity( identity( returns the identity matrix of dimension rows dimension columns. identity(dimension) randM( randM( (create random matrix) returns a rows columns random matrix of integers , L9 and 9. The seed value stored to the rand function controls the values (Chapter 2). randM(rows,columns) Matrices 10-13 augment( augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows. augment(matrixA,matrixB) Matr4list( Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns. Matr4list(matrix,listnameA,...,listname n) & Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix. Matr4list(matrix,column#,listname) & List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal, List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(listA,...,list n,matrixname) & 10-14 Matrices cumSum( cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom. cumSum(matrix) Row Operations MATRX MATH menu items A through F are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRX NAMES menu. ref(, rref( ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. ref(matrix) rref( (reduced row-echelon form) returns the reduced rowechelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. rref(matrix) Matrices 10-15 rowSwap( rowSwap( returns a matrix. It swaps rowA and rowB of matrix. rowSwap(matrix,rowA,rowB) row+( row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB. row+(matrix,rowA,rowB) row( row( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results in row. row(value,matrix,row) row+( row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB. row+(value,matrix,rowA,rowB) 10-16 Matrices 11 Contents Lists Getting Started: Generating a Sequence .................. 11-2 Naming Lists ............................................. 11-3 Storing and Displaying Lists ............................. 11-4 Entering List Names ..................................... 11-6 Attaching Formulas to List Names ....................... 11-7 Using Lists in Expressions ............................... 11-9 LIST OPS Menu .......................................... 11-10 LIST MATH Menu ........................................ 11-17 Lists 11-1 Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A2. Store the results to a usercreated list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press y [LIST] ~ to display the LIST OPS menu. 2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location. 3. Press 1 [A] [A] 1 8 1 to enter the sequence. 4. Press , and then press y to turn on alpha-lock. Press [S] [E] [Q], and then press to turn off alpha-lock. Press 1 to complete the list name. 5. Press to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. 6. Press y [LIST] to display the LIST NAMES menu. Press to paste SEQ1 to the current cursor location. (If SEQ1 is not item 1 on your LIST NAMES menu, move the cursor to SEQ1 before you press .) 7. Press to display the MATH menu. Press 1 to select 1:4Frac, which pastes 4Frac to the current cursor location. 8. Press to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. 11-2 Lists Naming Lists Using TI-83 List Names L1 through L6 The TI-83 has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names L1 through L6 are on the keyboard above the numeric keys through . To paste one of these names to a valid screen, press y, and then press the appropriate key. L1 through L6 are stored in stat list editor columns 1 through 6 when you reset memory. To create a list name on the home screen, follow these steps. 1. Press y [ { ], enter one or more list elements, and then press y [ } ]. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions. Creating a List Name on the Home Screen 2. Press . 3. Press [letter from A to Z or q] to enter the first letter of the name. 4. Enter zero to four letters, q, or numbers to complete the name. 5. Press . The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the LIST NAMES menu. Note: If you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12). You also can create a list name in these four places. At the Name= prompt in the stat list editor At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt in the inferential stat editors On the home screen using SetUpEditor You can create as many list names as your TI-83 memory has space to store. Lists 11-3 Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. Use braces and on the home screen. Use the stat list editor (Chapter 12). The maximum dimension of a list is 999 elements. Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter real(listname)!listname. Displaying a List on the Home Screen To display the elements of a list on the home screen, enter the name of the list (preceded by if necessary; see page 11.16), and then press . An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. 11-4 Lists Copying One List to Another To copy a list, store it to another list. Accessing a List Element You can store a value to or recall a value from a specific list element. You can store to any element within the current list dimension or one element beyond. listname(element) Deleting a List from Memory To delete lists from memory, including L1 through L6, use the MEMORY DELETE FROM secondary menu (Chapter 18). Resetting memory restores L1 through L6. Removing a list from the stat list editor does not delete it from memory. You can use lists to graph a family of curves (Chapter 3). Using Lists in Graphing Lists 11-5 Entering List Names Using the LIST NAMES Menu To display the LIST NAMES menu, press y [LIST]. Each item is a user-created list name. LIST NAMES menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particular alpha character or q, press [letter from A to Z or q]. Tip: From the top of a menu, press } to move to the bottom. From the bottom, press to move to the top. Note: The LIST NAMES menu omits list names L1 through L6. Enter L1 through L6 directly from the keyboard (page 11.3). When you select a list name from the LIST NAMES menu, the list name is pasted to the current cursor location. The list name symbol precedes a list name when the name is pasted where non-list name data also is valid, such as the home screen. The symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor's Name= prompt or the stat plot editor's XList: and YList: prompts. Entering a UserCreated List Name Directly To enter an existing list name directly, follow these steps. 1. Press y [LIST] ~ to display the LIST OPS menu. 2. Select B:, which pastes to the current cursor location. is not always necessary (page 11.16). Note: You also can paste to the current cursor location from the CATALOG (Chapter 15). 3. Enter the characters that comprise the list name. 11-6 Lists Attaching Formulas to List Names Attaching a Formula to a List Name You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list. When anything in the attached formula changes, the list to which the formula is attached is updated automatically. When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated. When you edit the formula itself, all elements in the list to which the formula is attached are updated. For example, the first screen below shows that elements are stored to L3, and the formula L3+10 is attached to the list name ADD10. The quotation marks designate the formula to be attached to ADD10. Each element of ADD10 is the sum of an element in L3 and 10. The next screen shows another list, L4. The elements of L4 are the sum of the same formula that is attached to L3. However, quotation marks are not entered, so the formula is not attached to L4. On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and then redisplays L3. The last screen shows that editing L3 updated ADD10, but did not change L4. This is because the formula L3+10 is attached to ADD10, but it is not attached to L4. Note: To view a formula that is attached to a list name, use the stat list editor (Chapter 12). Lists 11-7 Attaching a Formula to a List on the Home Screen or in a Program To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps. 1. Press , enter the formula (which must resolve to a list), and press again. Note: When you include more than one list name in a formula, each list must have the same dimension. 2. Press . 3. Enter the name of the list to which you want to attach the formula. Press y, and then enter a TI-83 list name L1 through L6. Press y [LIST] and select a user.created list name from the LIST NAMES menu. Enter a user.created list name directly using (page 11.16). 4. Press . Note: The stat list editor displays a formula-lock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists. Detaching a Formula from a List You can detach (clear) an attached formula from a list in any of three ways. Enter ""!listname on the home screen. Edit any element of a list to which a formula is attached. Use the stat list editor (Chapter 12). Note: You also can use ClrList or ClrAllList to detach a formula from a list (Chapter 18). 11-8 Lists Using Lists in Expressions Using a List in an Expression You can use lists in an expression in any of three ways. When you press , any expression is evaluated for each list element, and a list is displayed. Use L1L6 or any user-created list name in an expression. Enter the list elements directly (step 1 on page 11.3). Use y [RCL] to recall the contents of the list into an expression at the cursor location (Chapter 1). & Note: You must paste user-created list names to the Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using . Using Lists with Math Functions You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed. When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as L1 in ({1,0,L1}), is ignored. This returns an error. This graphs X(1) and X(0), but skips X(L1). When you use two lists with a two-argument function, the dimension of each list must be the same. The function is evaluated for corresponding elements. When you use a list and a value with a two-argument function, the value is used with each element in the list. Lists 11-9 LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y [LIST] ~. NAMES OPS MATH 1:SortA( 2:SortD( 3:dim( 4:Fill( 5:seq( 6:cumSum( 7: @List( 8:Select( 9:augment( 0:List4matr( A:Matr4list( B: Sorts lists in ascending order. Sorts lists in descending order. Sets the list dimension. Fills all elements with a constant. Creates a sequence. Returns a list of cumulative sums. Returns difference of successive elements. Selects specific data points. Concatenates two lists. Stores a list to a matrix. Stores a matrix to a list. Designates the list-name data type. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values. SortD( (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus). With one list, SortA( and SortD( sort the elements of listname and update the list in memory. SortA(listname) SortD(listname) With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. All lists must have the same dimension. SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: In the example, 5 is the first element in L4, and 1 is the first element in L5. After SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1 becomes the second element of L5. Note: SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu (Chapter 12). 11-10 Lists Using dim( to Find List Dimensions dim( (dimension) returns the length (number of elements) of list. dim(list) Using dim( to Create a List You can use dim( with to create a new listname with dimension length from 1 to 999. The elements are zeros. length!dim(listname) Using dim( to Redimension a List You can use dim with to redimension an existing listname to dimension length from 1 to 999. The elements in the old listname that are within the new dimension are not changed. Extra list elements are filled by 0. Elements in the old list that are outside the new dimension are deleted. length!dim(listname) Fill( Fill( replaces each element in listname with value. Fill(value,listname) Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10). Lists 11-11 seq( seq( (sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1. seq( is not valid within expression. seq(expression,variable,begin,end[,increment]) cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers. cumSum(list) @List( @List( returns a list containing the differences between consecutive elements in list. @List subtracts the first element in list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list. list elements can be a real or complex numbers. @List(list) Select( Select( selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, xlistname and ylistname. For example, you can use Select( to select and then analyze a portion of plotted CBL 2/CBL or CBR data. Select(xlistname,ylistname) Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window (page 11.13). 11-12 Lists Before Using Select( Before using Select(, follow these steps. 1. Create two list names and enter the data. 2. Turn on a stat plot, select " (scatter plot) or (xyLine), and enter the two list names for Xlist: and Ylist: (Chapter 12). 3. Use ZoomStat to plot the data (Chapter 3). Using Select( to Select Data Points from a Plot To select data points from a scatter plot or xyLine plot, follow these steps. 1. Press y [LIST] ~ 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to the home screen. 2. Enter xlistname, press , enter ylistname, and then press to designate list names into which you want the selected data to be stored. 3. Press . The graph screen is displayed with Left Bound? in the bottom-left corner. 4. Press } or (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points. 5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound. Lists 11-13 6. Press . A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottomleft corner. 7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press . The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor. Note: The two new lists (xlistname and ylistname) will include the points you select as left bound and right bound. Also, left-bound x-value right-bound x-value must be true. 11-14 Lists augment( augment( concatenates the elements of listA and listB. The list elements can be real or complex numbers. augment(listA,listB) List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(list1,list2, . . . ,list n,matrixname) & Lists 11-15 Matr4list( Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then Matr4list( ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname arguments, then Matr4list( ignores extra matrix columns. Matr4list(matrix,listname1,listname2, . . . ,listname n) & Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter a column# after matrix. Matr4list(matrix,column#,listname) & preceding one to five characters identifies those characters as a user-created listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q. listname Generally, must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the , the TI-83 may misinterpret a user-created list name as implied multiplication of two or more characters. need not precede a user-created list name where a list name is the only valid input, for example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor. If you enter where it is not necessary, the TI-83 will ignore the entry. 11-16 Lists LIST MATH Menu LIST MATH Menu To display the LIST MATH menu, press y [LIST] |. NAMES OPS MATH 1: min( 2: max( 3: mean( 4: median( 5: sum( 6: prod( 7: stdDev( 8: variance( Returns minimum element of a list. Returns maximum element of a list. Returns mean of a list. Returns median of a list. Returns sum of elements in a list. Returns product of elements in list. Returns standard deviation of a list. Returns the variance of a list. min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. For a complex list, the element with smallest or largest magnitude (modulus) is returned. min(listA[,listB]) max(listA[,listB]) Note: min( and max( are the same as min( and max( on the MATH NUM menu. mean(, median( mean( returns the mean value of list. median( returns the median value of list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. mean(list[,freqlist]) median(list[,freqlist]) Lists 11-17 sum(, prod( sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers. prod( returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers. sum(list[,start,end]) prod(list[,start,end]) Sums and Products of Numeric Sequences You can combine sum( or prod( with seq( to obtain: upper Gexpression(x) expression(x) x=lower x=lower To evaluate G 2 (N1) from N=1 to 4: upper stdDev(, variance( stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. variance( returns the variance of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. stdDev(list[,freqlist]) variance(list[,freqlist]) 11-18 Lists 12 Contents Statistics Getting Started: Pendulum Lengths and Periods ......... 12-2 Setting Up Statistical Analyses ........................... 12-10 Using the Stat List Editor ................................ 12-11 Attaching Formulas to List Names ....................... 12-14 Detaching Formulas from List Names .................... 12-16 Switching Stat List Editor Contexts ...................... 12-17 Stat List Editor Contexts ................................. 12-18 STAT EDIT Menu ........................................ 12-20 Regression Model Features .............................. 12-22 STAT CALC Menu........................................ 12-24 Statistical Variables ...................................... 12-29 Statistical Analysis in a Program ......................... 12-30 Statistical Plotting ....................................... 12-31 Statistical Plotting in a Program ......................... 12-37 Statistics 12-1 Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum's period for each of 12 string lengths.* Length (cm) Time (sec) 6.5 11.0 13.2 15.0 18.0 23.1 24.4 26.6 30.5 34.3 37.6 41.5 1. Press z to set Func graphing mode. 2. Press ... 5 to select 5:SetUpEditor. SetUpEditor is pasted to the home screen. 0.51 0.68 0.73 0.79 0.88 0.99 1.01 1.08 1.13 1.26 1.28 1.32 Press . This removes lists from stat list editor columns 1 through 20, and then stores lists L1 through L6 in columns 1 through 6. Note: Removing lists from the stat list editor does not delete them from memory. 3. Press ... 1 to select 1:Edit from the STAT EDIT menu. The stat list editor is displayed. If elements are stored in L1 and L2, press } to move the cursor onto L1, and then press ` ~ } ` to clear both lists. Press | to move the rectangular cursor back to the first row in L1. *This example is quoted and adapted from Contemporary Precalculus Through Applications, by the North Carolina School of Science and Mathematics, by permission of Janson Publications, Inc., Dedham, MA. 1-800-322-MATH. 1992. All rights reserved. 12-2 Statistics 4. Press 6 5 to store the first pendulum string length (6.5 cm) in L1. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table on page 12.2. 5. Press ~ to move the rectangular cursor to the first row in L2. Press 51 to store the first time measurement (.51 sec) in L2. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table on page 12.2. 6. Press o to display the Y= editor. If necessary, press ` to clear the function Y1. As necessary, press }, , and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press , |, and to deselect functions. 7. Press y [STAT PLOT] 1 to select 1:Plot1 from the STAT PLOTS menu. The stat plot editor is displayed for plot 1. 8. Press to select On, which turns on plot 1. Press to select " (scatter plot). Press y [L1] to specify Xlist:L1 for plot 1. Press y [L2] to specify Ylist:L2 for plot 1. Press ~ to select + as the Mark for each data point on the scatter plot. 9. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the time-versus-length data. Statistics 12-3 Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data. 10. Press ... ~ 4 to select 4:LinReg(ax+b) (linear regression model) from the STAT CALC menu. LinReg(ax+b) is pasted to the home screen. 11. Press y [L1] y [L2] . Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to LinReg(ax+b). 12. Press to execute LinReg(ax+b). The linear regression for the data in L1 and L2 is calculated. Values for a and b are displayed on the home screen. The linear regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID, which becomes an item on the LIST NAMES menu. 13. Press s. The regression line and the scatter plot are displayed. 12-4 Statistics The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit. 14. Press ... 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y [INS]. An unnamed column is displayed in column 3; L3, L4, L5, and L6 shift right one column. The Name= prompt is displayed in the entry line, and alpha-lock is on. 15. Press y [LIST] to display the LIST NAMES menu. If necessary, press to move the cursor onto the list name RESID. 16. Press to select RESID and paste it to the stat list editor's Name= prompt. 17. Press . RESID is stored in column 3 of the stat list editor. Press repeatedly to examine the residuals. Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern more clearly. Statistics 12-5 18. Press y [STAT PLOT] 2 to select 2:Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for plot 2. 19. Press to select On, which turns on plot 2. Press to select " (scatter plot). Press y [L1] to specify Xlist:L1 for plot 2. Press [R] [E] [S] [I] [D] (alpha-lock is on) to specify Ylist:RESID for plot 2. Press to select > as the mark for each data point on the scatter plot. 20. Press o to display the Y= editor. Press | to move the cursor onto the = sign, and then press to deselect Y1. Press } to turn off plot 1. 21. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals. Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals. 12-6 Statistics The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a xb. 22. Press o to display the Y= editor. Press ` to clear the linear regression equation from Y1. Press } to turn on plot 1. Press ~ to turn off plot 2. 23. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and the original scatter plot of time-versuslength data (plot 1) is displayed. 24. Press ... ~ [A] to select A:PwrReg from the STAT CALC menu. PwrReg is pasted to the home screen. Press y [L1] y [L2] . Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to PwrReg. 25. Press to calculate the power regression. Values for a and b are displayed on the home screen. The power regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID. 26. Press s. The regression line and the scatter plot are displayed. Statistics 12-7 The new function y=.192x.522 appears to fit the data well. To get more information, examine a residual plot. 27. Press o to display the Y= editor. Press | to deselect Y1. Press } to turn off plot 1. Press ~ to turn on plot 2. Note: Step 19 defined plot 2 to plot residuals (RESID) versus string length (L1). 28. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals. The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases. To see the magnitudes of the residuals, continue with these steps. 29. Press r. Press ~ and | to trace the data. Observe the values for Y at each point. With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude. 12-8 Statistics Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps. 30. Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. Y1 is pasted to the home screen. 31. Press 20 to enter a string length of 20 cm. Press to calculate the predicted time of about 0.92 seconds. Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value. 32. Press y [ENTRY] to recall the Last Entry. Press | | | 5 to change the string length to 50 cm. 33. Press to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate. Note: You also can make predictions using the table with the TABLE SETUP settings Indpnt:Ask and Depend:Auto (Chapter 7). Statistics 12-9 Setting Up Statistical Analyses Using Lists to Store Data Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-83 has six list variables in memory, L1 through L6, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11). To set up a statistical analysis, follow these steps. Read the chapter for details. 1. Enter the statistical data into one or more lists. 2. Plot the data. 3. Calculate the statistical variables or fit a model to the data. 4. Graph the regression equation for the plotted data. 5. Graph the residuals list for the given regression model. Setting Up a Statistical Analysis Displaying the Stat List Editor The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names from the stat list editor. To display the stat list editor, press ..., and then select 1:Edit from the STAT EDIT menu. The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the top-right corner. The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context (page 12.17). The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element. 12-10 Statistics Using the Stat List Editor Entering a List Name in the Stat List Editor To enter a list name in the stat list editor, follow these steps. 1. Display the Name= prompt in the entry line in either of two ways. Move the cursor onto the list name in the column where you want to insert a list, and then press y [INS]. An unnamed column is displayed and the remaining lists shift right one column. Press } until the cursor is on the top line, and then press ~ until you reach the unnamed column. Note: If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column. The Name= prompt is displayed and alpha-lock is on. 2. Enter a valid list name in any of four ways. Select a name from the LIST NAMES menu (Chapter 11). Enter L1, L2, L3, L4, L5, or L6 from the keyboard. Enter an existing user-created list name directly from the keyboard. Enter a new user-created list name (page 12.12). 3. Press or to store the list name and its elements, if any, in the current column of the stat list editor. To begin entering, scrolling, or editing list elements, press . The rectangular cursor is displayed. Note: If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly. Statistics 12-11 Creating a Name in the Stat List Editor To create a name in the stat list editor, follow these steps. 1. Follow step 1 on page 12.11 to display the Name= prompt. 2. Press [letter from A to Z or q] to enter the first letter of the name. The first character cannot be a number. 3. Enter zero to four letters, q, or numbers to complete the new user-created list name. List names can be one to five characters long. 4. Press or to store the list name in the current column of the stat list editor. The list name becomes an item on the LIST NAMES menu (Chapter 11). Removing a List from the Stat List Editor To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor. Note: To delete a list name from memory, use the MEMORY DELETE:List selection screen (Chapter 18). Removing All Lists and Restoring L1 through L6 You can remove all user-created lists from the stat list editor and restore list names L1 through L6 to columns 1 through 6 in either of two ways. Use SetUpEditor with no arguments (page 12.21). Reset all memory (Chapter 18). You can clear all elements from a list in any of five ways. Use ClrList to clear specified lists (page 12.20). In the stat list editor, press } to move the cursor onto a list name, and then press ` . In the stat list editor, move the cursor onto each element, and then press { one by one. On the home screen or in the program editor, enter 0!dim(listname) to set the dimension of listname to 0 (Chapter 11). Use ClrAllLists to clear all lists in memory (Chapter 18). Clearing All Elements from a List 12-12 Statistics Editing a List Element To edit a list element, follow these steps. 1. Move the rectangular cursor onto the element you want to edit. 2. Press to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing . When you enter the first character, the current value is cleared automatically. 3. Edit the element in the entry line. Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically. Press ~ to move the cursor to the character before which you want to insert, press y [INS], and then enter one or more characters. Press ~ to move the cursor to a character you want to delete, and then press { to delete the character. To cancel any editing and restore the original element at the rectangular cursor, press ` . Note: You can enter expressions and variables for elements. 4. Press , }, or to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory immediately. Statistics 12-13 Attaching Formulas to List Names Attaching a Formula to a List Name in Stat List Editor You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names. To attach a formula to a list name that is stored in the stat list editor, follow these steps. 1. Press ... to display the stat list editor. 2. Press } to move the cursor to the top line. 3. Press | or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula. Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press , and then edit the formula. 4. Press , enter the formula, and press . Note: If you do not use quotation marks, the TI-83 calculates and displays the same initial list of answers, but does not attach the formula for future calculations. Note: Any user-created list name referenced in a formula must be preceded by an symbol (Chapter 11). 5. Press . The TI-83 calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached. lock symbol 12-14 Statistics Using the Stat List Editor When FormulaGenerated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-83 updates the corresponding element in the list to which the formula is attached (Chapter 11). When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-83 takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view. Tip: To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed. Handling Errors Resulting from Attached Formulas On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references. All elements of a list referenced by an attached formula must be valid for the attached formula. For example, if Real number mode is set and the attached formula is log(L1), then each element of L1 must be greater than 0, since the logarithm of a negative number returns a complex result. Tip: If an error menu is returned when you attempt to display a formula-generated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press ` to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list. If you do not want to clear the formula, you can select 1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listname(element#) (Chapter 11). Statistics 12-15 Detaching Formulas from List Names Detaching a Formula from a List Name You can detach (clear) a formula from a list name in any of four ways. In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press ` . All list elements remain, but the formula is detached and the lock symbol disappears. In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press , edit the element, and then press . The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain. Use ClrList (page 12.20). All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain. Use ClrAllLists (Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain. As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-83 protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list. Because of the protection feature, you must press before you can edit an element of a formula-generated list. The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you must first detach the formula in any of the ways described above. Editing an Element of a FormulaGenerated List 12-16 Statistics Switching Stat List Editor Contexts Stat List Editor Contexts The stat list editor has four contexts. View-elements context View-names context Edit-elements context Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select 1:Edit from the STAT EDIT menu and follow these steps. 1. Press } to move the cursor onto a list name. You are now in view-names context. Press ~ and | to view list names stored in other stat list editor columns. 2. Press . You are now in edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces ( { } )in the entry line. Press ~ and | to view more list elements. 3. Press again. You are now in view-elements context. Press ~, |, , and } to view other list elements. The current element's full value is displayed in the entry line. 4. Press again. You are now in edit-elements context. You may edit the current element in the entry line. 5. Press } until the cursor is on a list name, then press y [INS]. You are now in enter-name context. 6. Press `. You are now in view-names context. 7. Press . You are now back in view-elements context. Statistics 12-17 Stat List Editor Contexts View-Elements Context In view-elements context, the entry line displays the list name, the current element's place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (...) indicates that the element continues beyond 12 characters. To page down the list six elements, press . To page up six elements, press }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y [INS]. 0 is the default value for a new element. Edit-Elements Context In edit-elements context, the data displayed in the entry line depends on the previous context. When you switch to edit-elements context from viewelements context, the full value of the current element is displayed. You can edit the value of this element, and then press and } to edit other list elements. & When you switch to edit-elements context from viewnames context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list. & Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context. 12-18 Statistics View-Names Context In view-names context, the entry line displays the list name and the list elements. To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory. To insert a name in the current column, press y [INS]. Remaining columns shift to the right one column. Enter-Name Context In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on. At the Name= prompt, you can create a new list name, paste a list name from L1 to L6 from the keyboard, or paste an existing list name from the LIST NAMES menu (Chapter 11). The symbol is not required at the Name= prompt. To leave enter-name context without entering a list name, press `. The stat list editor switches to view-names context. Statistics 12-19 STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT menu, press .... EDIT CALC TESTS 1: Edit... 2: SortA( 3: SortD( 4: ClrList 5: SetUpEditor Displays the stat list editor. Sorts a list in ascending order. Sorts a list in descending order. Deletes all elements of a list. Stores lists in the stat list editor. Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values. SortD( (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus). SortA( and SortD( each can sort in either of two ways. With one listname, SortA( and SortD( sort the elements in listname and update the list in memory. With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. This lets you sort two-variable data on X and keep the data pairs together. All lists must have the same dimension. The sorted lists are updated in memory. SortA(listname) SortD(listname) SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu. ClrList ClrList clears (deletes) from memory the elements of one or more listnames. ClrList also detaches any formula attached to a listname. ClrList listname1,listname2,...,listname n Note: To clear from memory all elements of all list names, use ClrAllLists (Chapter 18). 12-20 Statistics SetUpEditor With SetUpEditor you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames. SetUpEditor [listname1,listname2,...,listname n] SetUpEditor with one to 20 listnames removes all list names from the stat list editor and then stores listnames in the stat list editor columns in the specified order, beginning in column 1. If you enter a listname that is not stored in memory already, then listname is created and stored in memory; it becomes an item on the LIST NAMES menu. Restoring L1 through L6 to the Stat List Editor SetUpEditor with no listnames removes all list names from the stat list editor and restores list names L1 through L6 in the stat list editor columns 1 through 6. Statistics 12-21 Regression Model Features Regression Model Features STAT CALC menu items 3 through C are regression models (page 12.24). The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models. Automatic Residual List When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name RESID. RESID becomes an item on the LIST NAMES menu (Chapter 11). The TI-83 uses the formula below to compute RESID list elements. The next section describes the variable RegEQ. RESID = Ylistname N RegEQ(Xlistname) Automatic Regression Equation Each regression model has an optional argument, regequ, for which you can specify a Y= variable such as Y1. Upon execution, the regression equation is stored automatically to the specified Y= variable and the Y= function is selected. Regardless of whether you specify a Y= variable for regequ, the regression equation always is stored to the TI-83 variable RegEQ, which is item 1 on the VARS Statistics EQ secondary menu. Note: For the regression equation, you can use the fixed-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit. 12-22 Statistics Diagnostics Display Mode When you execute some regression models, the TI-83 computes and stores diagnostics values for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient of determination). r and r2 are computed and stored for these regression models. LinReg(ax+b) LinReg(a+bx) LnReg ExpReg PwrReg R2 is computed and stored for these regression models. QuadReg r2 CubicReg QuartReg The r and that are computed for LnReg, ExpReg, and PwrReg are based on the linearly transformed data. For example, for ExpReg (y=ab^x), r and r2 are computed on ln y=ln a+x(ln b). By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the DiagnosticOn or DiagnosticOff instruction. Each instruction is in the CATALOG (Chapter 15). Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y [CATALOG], and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press to set the mode. When DiagnosticOn is set, diagnostics are displayed with the results when you execute a regression model. When DiagnosticOff is set, diagnostics are not displayed with the results when you execute a regression model. Statistics 12-23 STAT CALC Menu STAT CALC Menu To display the STAT CALC menu, press ... ~. EDIT CALC TESTS 1: 1-Var Stats 2: 2-Var Stats 3: Med-Med 4: LinReg(ax+b) 5: QuadReg 6: CubicReg 7: QuartReg 8: LinReg(a+bx) 9: LnReg 0: ExpReg A: PwrReg B: Logistic C: SinReg Calculates 1-variable statistics. Calculates 2-variable statistics. Calculates a median-median line. Fits a linear model to data. Fits a quadratic model to data. Fits a cubic model to data. Fits a quartic model to data. Fits a linear model to data. Fits a logarithmic model to data. Fits an exponential model to data. Fits a power model to data. Fits a logistic model to data. Fits a sinusoidal model to data. For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified, then the default list names are L1 and L2. If you do not specify freqlist, then the default is 1 occurrence of each list element. Frequency of Occurrence for Data Points For most STAT CALC menu items, you can specify a list of data occurrences, or frequencies (freqlist). Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing. For example, if L1={15,12,9,14} and FREQ={1,4,1,3}, then the TI-83 interprets the instruction 1.Var Stats L1, FREQ to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times. Each element in freqlist must be , 0, and at least one element must be > 0. Noninteger freqlist elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, if freqlist contains noninteger frequencies, Sx and Sy are undefined; values are not displayed for Sx and Sy in the statistical results. 12-24 Statistics 1-Var Stats 1.Var Stats (one-variable statistics) analyzes data with one measured variable. Each element in freqlist is the frequency of occurrence for each corresponding data point in Xlistname. freqlist elements must be real numbers > 0. 1.Var Stats [Xlistname,freqlist] 2-Var Stats 2.Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for each data pair (Xlistname,Ylistname). 2.Var Stats [Xlistname,Ylistname,freqlist] Med-Med (ax+b) Med.Med (median-median) fits the model equation y=ax+b to the data using the median-median line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3. Med.Med displays values for a (slope) and b (y-intercept). Med.Med [Xlistname,Ylistname,freqlist,regequ] LinReg (ax+b) LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit. It displays values for a (slope) and b (y-intercept); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ] QuadReg (ax 2+bx+c) QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required. QuadReg [Xlistname,Ylistname,freqlist,regequ] Statistics 12-25 CubicReg (ax 3+bx 2+cx+d) CubicReg (cubic regression) fits the third-degree polynomial y=ax 3+bx 2+cx+d to the data. It displays values for a, b, c, and d; when DiagnosticOn is set, it also displays a value for R2. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required. CubicReg [Xlistname,Ylistname,freqlist,regequ] QuartReg (ax 4+bx 3+cx 2+ dx+e) QuartReg (quartic regression) fits the fourth-degree polynomial y=ax 4+bx 3+cx 2+dx+e to the data. It displays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays a value for R2. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required. QuartReg [Xlistname,Ylistname,freqlist,regequ] LinReg (a+bx) LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data using a least-squares fit. It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ] LnReg (a+b ln(x)) LnReg (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a least-squares fit and transformed values ln(x) and y. It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. LnReg [Xlistname,Ylistname,freqlist,regequ] ExpReg (ab x) ExpReg (exponential regression) fits the model equation y=abx to the data using a least-squares fit and transformed values x and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. ExpReg [Xlistname,Ylistname,freqlist,regequ] 12-26 Statistics PwrReg (axb) PwrReg (power regression) fits the model equation y=axb to the data using a least-squares fit and transformed values ln(x) and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. PwrReg [Xlistname,Ylistname,freqlist,regequ] Logistic c / (1+aeLbx) Logistic fits the model equation y=c / (1+aeLbx) to the data using an iterative least-squares fit. It displays values for a, b, and c. Logistic [Xlistname,Ylistname,freqlist,regequ] SinReg a sin(bx+c)+d SinReg (sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using an iterative least-squares fit. It displays values for a, b, c, and d. At least four data points are required. At least two data points per cycle are required in order to avoid aliased frequency estimates. SinReg [iterations,Xlistname,Ylistname,period,regequ] iterations is the maximum number of times the algorithm will iterate to find a solution. The value for iterations can be an integer , 1 and 16; if not specified, the default is 3. The algorithm may find a solution before iterations is reached. Typically, larger values for iterations result in longer execution times and better accuracy for SinReg, and vice versa. A period guess is optional. If you do not specify period, the difference between time values in Xlistname must be equal and the time values must be ordered in ascending sequential order. If you specify period, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal. Note: The output of SinReg is always in radians, regardless of the Radian/Degree mode setting. A SinReg example is shown on the next page. Statistics 12-27 SinReg Example: Daylight Hours in Alaska for One Year Compute the regression model for the number of hours of daylight in Alaska during one year. & & 1 period With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways. Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle. Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N. After your first attempt to use SinReg and the default value for iterations to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute SinReg 16,Xlistname,Ylistname,2p / b where b is the value obtained from the previous SinReg execution. 12-28 Statistics Statistical Variables The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select 5:Statistics. Then select the VARS menu shown in the column below under VARS menu. If you edit a list or change the type of analysis, all statistical variables are cleared. Variables 1.Var Stats v Gx Gx2 Sx sx n 2.Var Stats v Gx Gx2 Sx sx n w Gy Gy2 Sy sy Gxy minX maxX minX maxX minY maxY Q1 Med Q3 a, b a, b, c, d, e r r 2, R 2 RegEQ x1, y1, x2, y2, x3, y3 Other VARS menu XY G G XY XY XY XY G G XY XY G XY XY XY XY PTS PTS PTS EQ EQ EQ EQ EQ PTS mean of x values sum of x values sum of x2 values sample standard deviation of x population standard deviation of x number of data points mean of y values sum of y values sum of y2 values sample standard deviation of y population standard deviation of y sum of x ... y minimum of x values maximum of x values minimum of y values maximum of y values 1st quartile median 3rd quartile regression/fit coefficients polynomial, Logistic, and SinReg coefficients correlation coefficient coefficient of determination regression equation summary points (Med.Med only) Q1 and Q3 The first quartile (Q1) is the median of points between minX and Med (median). The third quartile (Q3) is the median of points between Med and maxX. Statistics 12-29 Statistical Analysis in a Program Entering Stat Data You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11). Statistical Calculations To perform a statistical calculation from a program, follow these steps. 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of the lists to use in the calculation. Separate the list names with a comma. 3. Enter a comma and then the name of a Y= variable, if you want to store the regression equation to a Y= variable. 12-30 Statistics Statistical Plotting Steps for Plotting You can plot statistical data that is stored in lists. The six Statistical Data in types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability Lists plot. You can define up to three plots. To plot statistical data in lists, follow these steps. 1. Store the stat data in one or more lists. 2. Select or deselect Y= functions as appropriate. 3. Define the stat plot. 4. Turn on the plots you want to display. 5. Define the viewing window. 6. Display and explore the graph. " (Scatter) Scatter plots plot the data points from Xlist and Ylist as coordinate pairs, showing each point as a box ( > ), cross ( + ), or dot ( ). Xlist and Ylist must be the same length. You can use the same list for Xlist and Ylist. (xyLine) xyLine is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists before you plot them (page 12.20). Statistics 12-31 (Histogram) Histogram plots one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) Xscl 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. (ModBoxplot) ModBoxplot (modified box plot) plots one-variable data, like the regular box plot, except points that are 1.5 Interquartile Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile Q3 and the first quartile Q1.) These points are plotted individually beyond the whisker, using the Mark (> or + or ) you select. You can trace these points, which are called outliers. The prompt for outlier points is x=, except when the outlier is the maximum point (maxX) or the minimum point (minX). When outliers exist, the end of each whisker will display x=. When no outliers exist, minX and maxX are the prompts for the end of each whisker. Q1, Med (median), and Q3 define the box (page 12.29). Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. 12-32 Statistics (Boxplot) Boxplot (regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (maxX). The box is defined by Q1, Med (median), and Q3 (page 12.29). Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. (NormProbPlot) NormProbPlot (normal probability plot) plots each observation X in Data List versus the corresponding quantile z of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal. Enter a valid list name in the Data List field. Select X or Y for the Data Axis setting. If you select X, the TI-83 plots the data on the x-axis and the z-values on the y-axis. If you select Y, the TI-83 plots the data on the y-axis and the z-values on the x-axis. Statistics 12-33 Defining the Plots To define a plot, follow these steps. 1. Press y [STAT PLOT]. The STAT PLOTS menu is displayed with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected. 3. Press to select On if you want to plot the statistical data immediately. The definition is stored whether you select On or Off. 4. Select the type of plot. Each type prompts for the options checked in this table. Plot Type " Scatter xyLine Histogram ModBoxplot Boxplot NormProbPlot XList YList Mark Freq Data Data List Axis oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe oe 5. Enter list names or select options for the plot type. Xlist (list name containing independent data) Ylist (list name containing dependent data) Mark (> or + or ) Freq (frequency list for Xlist elements; default is 1) Data List (list name for NormProbPlot) Data Axis (axis on which to plot Data List) 12-34 Statistics Displaying Other Stat Plot Editors Each stat plot has a unique stat plot editor. The name of the current stat plot (Plot1, Plot2, or Plot3) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press . The stat plot editor for the selected plot is displayed, and the selected name remains highlighted. Turning On and Turning Off Stat Plots PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots. With one or more plot numbers (1, 2, and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified plots. PlotsOff [1,2,3] PlotsOn [1,2,3] Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3). Statistics 12-35 Defining the Viewing Window Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables. ZoomStat redefines the viewing window to display all statistical data points. When you trace a scatter plot or xyLine, tracing begins at the first element in the lists. When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column. When you trace a box plot, tracing begins at Med (the median). Press | to trace to Q1 and minX. Press ~ to trace to Q3 and maxX. When you press } or to move to another plot or to another Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel). The ExprOn/ExprOff format setting applies to stat plots (Chapter 3).When ExprOn is selected, the plot number and plotted data lists are displayed in the top-left corner. Tracing a Stat Plot 12-36 Statistics Statistical Plotting in a Program Defining a Stat Plot in a Program To display a stat plot from a program, define the plot, and then display the graph. To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press y [STAT PLOT] to display the STAT PLOTS menu. 2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location. 3. Press y [STAT PLOT] ~ to display the STAT TYPE menu. 4. Select the type of plot, which pastes the name of the plot type to the cursor location. Statistics 12-37 5. Press . Enter the list names, separated by commas. 6. Press y [STAT PLOT] | to display the STAT PLOT MARK menu. (This step is not necessary if you selected 3:Histogram or 5:Boxplot in step 4.) Select the type of mark (> or + or ) for each data point. The selected mark symbol is pasted to the cursor location. 7. Press to complete the command line. Displaying a Stat Plot from a Program To display a plot from a program, use the DispGraph instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3). 12-38 Statistics 13 Contents Inferential Statistics and Distributions Getting Started: Mean Height of a Population ............ 13-2 Inferential Stat Editors................................... 13-6 STAT TESTS Menu ...................................... 13-9 Inferential Statistics Input Descriptions .................. 13-26 Test and Interval Output Variables ....................... 13-28 Distribution Functions ................................... 13-29 Distribution Shading ..................................... 13-35 Inferential Statistics and Distributions 13-1 Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The 10 height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed mean of 165.1 cm. and a standard deviation of 6.35 cm. (randNorm(165.1,6.35,90) with a seed of 789). Height (in cm.) of Each of 10 Women 169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53 1. Press ... to display the stat list editor. Press } to move the cursor onto L1, and then press y [INS]. The Name= prompt is displayed on the bottom line. The cursor indicates that alpha-lock is on. The existing list name columns shift to the right. Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored. 2. Enter [H] [G] [H] [T] at the Name= prompt, and then press . The list to which you will store the women's height data is created. Press to move the cursor onto the first row of the list. HGHT(1)= is displayed on the bottom line. 3. Press 169 43 to enter the first height value. As you enter it, it is displayed on the bottom line. Press . The value is displayed in the first row, and the rectangular cursor moves to the next row. Enter the other nine height values the same way. 13-2 Inferential Statistics and Distributions 4. Press ... | to display the STAT TESTS menu, and then press until 8:TInterval is highlighted. 5. Press to select 8:TInterval. The inferential stat editor for TInterval is displayed. If Data is not selected for Inpt:, press | to select Data. Press and [H] [G] [H] [T] at the List: prompt (alpha-lock is on). Press 99 to enter a 99 percent confidence level at the C.Level: prompt. 6. Press to move the cursor onto Calculate, and then press . The confidence interval is calculated, and the TInterval results are displayed on the home screen. Interpret the results. The first line, (159.74,173.94), shows that the 99 percent confidence interval for the population mean is between about 159.74 cm. and 173.94 cm. This is about a 14.2 cm. spread. The .99 confidence level indicates that in a very large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 cm. (introduction; page 13.2), which is in the calculated interval. The second line gives the mean height of the sample used to compute this interval. The third line gives the sample standard deviation Sx. The bottom line gives the sample size n. Inferential Statistics and Distributions 13-3 To obtain a more precise bound on the population mean m of women's heights, increase the sample size to 90. Use a sample mean of 163.8 and sample standard deviation Sx of 7.1 calculated from the larger random sample (introduction; page 13.2). This time, use the Stats (summary statistics) input option. 7. Press ... | 8 to display the inferential stat editor for TInterval. Press ~ to select Inpt:Stats. The editor changes so that you can enter summary statistics as input. 8. Press 163 8 to store 163.8 to . Press 7 1 to store 7.1 to Sx. Press 90 to store 90 to n. 9. Press to move the cursor onto Calculate, and then press to calculate the new 99 percent confidence interval. The results are displayed on the home screen. If the height distribution among a population of women is normally distributed with a mean m of 165.1 cm. and a standard deviation of 6.35 cm., what height is exceeded by only 5 percent of the women (the 95th percentile)? 10. Press ` to clear the home screen. Press y [DISTR] to display the DISTR (distributions) menu. 13-4 Inferential Statistics and Distributions 11. Press 3 to paste invNorm( to the home screen. Press 95 165 1 6 35 . .95 is the area, 165.1 is , and 6.35 is . The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 cm. Now graph and shade the top 5 percent of the population. 12. Press p and set the window variables to these values. Xmin=145 Xmax=185 Xscl=5 Ymin=L.02 Ymax=.08 Yscl=0 Xres=1 13. Press y [DISTR] ~ to display the DISTR DRAW menu. 14. Press to paste ShadeNorm( to the home screen. Press y [ANS] 1 y [EE] 99 165 1 6 35 . Ans (175.5448205 from step 11) is the lower bound. 199 is the upper bound. The normal curve is defined by a mean of 165.1 and a standard deviation of 6.35. 15. Press to plot and shade the normal curve. Area is the area above the 95th percentile. low is the lower bound. up is the upper bound. Inferential Statistics and Distributions 13-5 Inferential Stat Editors Displaying the Inferential Stat Editors When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval's input requirements. Below is the inferential stat editor for T.Test. Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen. Using an Inferential Stat Editor To use an inferential stat editor, follow these steps. 1. Select a hypothesis test or confidence interval from the STAT TESTS menu. The appropriate editor is displayed. 2. Select Data or Stats input, if the selection is available. The appropriate editor is displayed. 3. Enter real numbers, list names, or expressions for each argument in the editor. 4. Select the alternative hypothesis (, <, or >) against which to test, if the selection is available. 5. Select No or Yes for the Pooled option, if the selection is available. 6. Select Calculate or Draw (when Draw is available) to execute the instruction. When you select Calculate, the results are displayed on the home screen. When you select Draw, the results are displayed in a graph. This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction. 13-6 Inferential Statistics and Distributions Select Data or Stats input Select an alternative hypothesis Enter values for arguments Select Calculate or Draw output Selecting Data or Stats Most inferential stat editors prompt you to select one of two types of input. (1.PropZInt and 2.PropZTest, 1.PropZInt and 2.PropZInt, c2.Test, and LinRegTTest do not.) Select Data to enter the data lists as input. Select Stats to enter summary statistics, such as , Sx, and n, as input. To select Data or Stats, move the cursor to either Data or Stats, and then press . Entering the Values for Arguments Inferential stat editors require a value for every argument. If you do not know what a particular argument symbol represents, see the tables on pages 13.26 and 13.27. When you enter values in any inferential stat editor, the TI.83 stores them in memory so that you can run many tests or intervals without having to reenter every value. Selecting an Alternative Hypothesis ( < >) Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses. The first is a alternative hypothesis, such as mm0 for the Z.Test. The second is a < alternative hypothesis, such as m1<m2 for the 2.SampTTest. The third is a > alternative hypothesis, such as p1>p2 for the 2.PropZTest. To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press . Inferential Statistics and Distributions 13-7 Selecting the Pooled Option Pooled (2.SampTTest and 2.SampTInt only) specifies whether the variances are to be pooled for the calculation. Select No if you do not want the variances pooled. Population variances can be unequal. Select Yes if you want the variances pooled. Population variances are assumed to be equal. To select the Pooled option, move the cursor to Yes, and then press . Selecting Calculate or Draw for a Hypothesis Test After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (Calculate) or on the graph screen (Draw). Calculate calculates the test results and displays the outputs on the home screen. Draw draws a graph of the test results and displays the test statistic and p-value with the graph. The window variables are adjusted automatically to fit the graph. To select Calculate or Draw, move the cursor to either Calculate or Draw, and then press . The instruction is immediately executed. Selecting Calculate for a Confidence Interval After you have entered all arguments in an inferential stat editor for a confidence interval, select Calculate to display the results. The Draw option is not available. When you press , Calculate calculates the confidence interval results and displays the outputs on the home screen. To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the CATALOG menu. Appendix A describes the input syntax for each hypothesis test and confidence interval instruction. Bypassing the Inferential Stat Editors Note: You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the CATALOG (Chapter 15) or the STAT TESTS menu. 13-8 Inferential Statistics and Distributions STAT TESTS Menu STAT TESTS Menu To display the STAT TESTS menu, press ... |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed. Most STAT TESTS instructions store some output variables to memory. Most of these output variables are in the TEST secondary menu (VARS menu; 5:Statistics). For a list of these variables, see page 13.28. EDIT CALC TESTS 1: Z-Test... Test for 1 m, known s 2: T-Test... Test for 1 m, unknown s 3: 2-SampZTest... Test comparing 2 m's, known s's 4: 2-SampTTest... Test comparing 2 m's, unknown s's 5: 1-PropZTest... Test for 1 proportion 6: 2-PropZTest... Test comparing 2 proportions 7: ZInterval... Confidence interval for 1 m, known s 8: TInterval... Confidence interval for 1 m, unknown s 9: 2-SampZInt... Conf. int. for diff. of 2 m's, known s's 0: 2-SampTInt... Conf. int. for diff. of 2 m's, unknown s's A: 1-PropZInt... Confidence int. for 1 proportion B: 2-PropZInt... Confidence int. for diff. of 2 props C: c2-Test... Chi-square test for 2-way tables D: 2-SampTest... Test comparing 2 s's E: LinRegTTest... t test for regression slope and r F: ANOVA( One-way analysis of variance Note: When a new test or interval is computed, all previous output variables are invalidated. Inferential Stat Editors for the STAT TESTS Instructions In this chapter, the description of each STAT TESTS instruction shows the unique inferential stat editor for that instruction with example arguments. Descriptions of instructions that offer the Data/Stats input choice show both types of input screens. Descriptions of instructions that do not offer the Data/Stats input choice show only one input screen. The description then shows the unique output screen for that instruction with the example results. Descriptions of instructions that offer the Calculate/Draw output choice show both types of screens: calculated and graphic results. Descriptions of instructions that offer only the Calculate output choice show the calculated results on the home screen. Inferential Statistics and Distributions 13-9 Z.Test Z.Test (one-sample z test; item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one of the alternatives below. Ha: mm0 (m:m0) Ha: m<m0 (m:<m0) Ha: m>m0 (m:>m0) In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , Calculated results: , , Drawn results: , Note: All examples on pages13.10 through 13.25 assume a fixeddecimal mode setting of 4 (Chapter 1). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. 13-10 Inferential Statistics and Distributions T.Test T.Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below. Ha: mm0 (m:m0) Ha: m<m0 (m:<m0) Ha: m>m0 (m:>m0) In the example: TEST={91.9 97.8 111.4 122.3 105.4 95} Data Stats Input: , Calculated results: , , Drawn results: , Inferential Statistics and Distributions 13-11 2.SampZTest 2.SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below. Ha: m1m2 (m1:m2) Ha: m1<m2 (m1:<m2) Ha: m1>m2 (m1:>m2) In the example: LISTA={154 109 137 115 140} LISTB={108 115 126 92 146} Data Stats Input: , Calculated results: , , Drawn results: , 13-12 Inferential Statistics and Distributions 2.SampTTest 2.SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below. Ha: m1m2 (m1:m2) Ha: m1<m2 (m1:<m2) Ha: m1>m2 (m1:>m2) In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data Stats Input: , Calculated results: , , Drawn results: , Inferential Statistics and Distributions 13-13 ) 1-PropZTest 1.PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1.PropZTest tests the null hypothesis H0: prop=p0 against one of the alternatives below. Ha: propp 0 (prop:p0) Ha: prop<p0 (prop:<p0) Ha: prop>p 0 (prop:>p0) Input: , Calculated results: , Drawn results: 13-14 Inferential Statistics and Distributions 2-PropZTest 2.PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). 2.PropZTest tests the null hypothesis H0: p1=p2 (using the pooled sample proportion ) against one of the alternatives below. Ha: p1p2 (p1:p2) Ha: p1<p2 (p1:<p2) Ha: p1>p2 (p1:>p2) Input: , Calculated results: , Drawn results: Inferential Statistics and Distributions 13-15 ZInterval ZInterval (one-sample z confidence interval; item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , Calculated results: , 13-16 Inferential Statistics and Distributions TInterval TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example: L6={1.6 1.7 1.8 1.9} Data Stats Input: , Calculated results: , Inferential Statistics and Distributions 13-17 2-SampZInt 2.SampZInt (two-sample z confidence interval; item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations ( s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level. In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146} Data Stats Input: , Calculated results: , 13-18 Inferential Statistics and Distributions 2-SampTInt 2.SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the userspecified confidence level. In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data Stats Input: , Calculated results: , Inferential Statistics and Distributions 13-19 ) 1-PropZInt 1.PropZInt (one-proportion z confidence interval; item A) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n. The computed confidence interval depends on the userspecified confidence level. Input: , Calculated results: 13-20 Inferential Statistics and Distributions 2-PropZInt 2.PropZInt (two-proportion z confidence interval; item B) computes a confidence interval for the difference between the proportion of successes in two populations (p1Np2). It takes as input the count of successes in each sample (x 1 and x 2) and the count of observations in each sample (n1 and n2). The computed confidence interval depends on the user-specified confidence level. Input: , Calculated results: Inferential Statistics and Distributions 13-21 c2-Test c2.Test (chi-square test; item C) computes a chi-square test for association on the two-way table of counts in the specified Observed matrix. The null hypothesis H 0 for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related. Before computing a c2.Test, enter the observed counts in a matrix. Enter that matrix variable name at the Observed: prompt in the c2.Test editor; default=[A]. At the Expected: prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=[B]. Note: Press ~ ~ 1 to select 1:[A] from the MATRX EDIT menu. Matrix editor: Input: , Note: Press [B] to display matrix [B]. Calculated results: , Drawn results: 13-22 Inferential Statistics and Distributions 2-SampTest 2.SampTest (two-sample -test; item D) computes an -test to compare two normal population standard deviations (s1 and s2). The population means and standard deviations are all unknown. 2.SampTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below. Ha: s1s2 (s1:s2) Ha: s1<s2 (s1:<s2) Ha: s1>s2 (s1:>s2) In the example: SAMP4={ 7 L4 18 17 L3 L5 SAMP5={ L1 12 L1 L3 3 L5 1 10 11 L2} 5 2 L11 L1 L3} Data Stats Input: , Calculated results: , , Drawn results: , Inferential Statistics and Distributions 13-23 LinRegTTest LinRegTTest (linear regression t test; item E) computes a linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0: b=0 (equivalently, r =0) against one of the alternatives below. Ha: b0 and r0 (b & r:0) Ha: b<0 and r<0 (b & r:<0) Ha: b>0 and r>0 (b & r:>0) The regression equation is automatically stored to RegEQ (VARS Statistics EQ secondary menu). If you enter a Y= variable name at the RegEQ: prompt, the calculated regression equation is automatically stored to the specified Y= equation. In the example below, the regression equation is stored to Y1, which is then selected (turned on). In the example: L3={38 56 59 64 74} L4={41 63 70 72 84} Input: , Calculated results: When LinRegTTest is executed, the list of residuals is created and stored to the list name RESID automatically. RESID is placed on the LIST NAMES menu. Note: For the regression equation, you can use the fix-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit. 13-24 Inferential Statistics and Distributions ANOVA( ANOVA( (one-way analysis of variance; item F) computes a one-way analysis of variance for comparing the means of two to 20 populations. The ANOVA procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H0: m1=m2=...=m k is tested against the alternative Ha: not all m1...mk are equal. ANOVA(list1,list2[,...,list20]) In the example: L1={7 4 6 6 5} L2={6 5 5 8 7} L3={4 7 6 7 6} Input: , Calculated results: Note: SS is sum of squares and MS is mean square. Inferential Statistics and Distributions 13-25 Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter. Input m0 s List Freq Calculate/Draw Description Hypothesized value of the population mean that you are testing. The known population standard deviation; must be a real number > 0. The name of the list containing the data you are testing. The name of the list containing the frequency values for the data in List. Default=1. All elements must be integers | 0. Determines the type of output to generate for tests and intervals. Calculate displays the output on the home screen. In tests, Draw draws a graph of the results. Summary statistics (mean, standard deviation, and sample size) for the one-sample tests and intervals. The known population standard deviation from the first population for the two-sample tests and intervals. Must be a real number > 0. The known population standard deviation from the second population for the two-sample tests and intervals. Must be a real number > 0. The names of the lists containing the data you are testing for the two-sample tests and intervals. Defaults are L1 and L2, respectively. The names of the lists containing the frequencies for the data in List1 and List2 for the two-sample tests and intervals. Defaults=1. All elements must be integers | 0. Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the two-sample tests and intervals. Specifies whether variances are to be pooled for 2.SampTTest and 2.SampTInt. No instructs the TI.83 not to pool the variances. Yes instructs the TI.83 to pool the variances. v, Sx, n s1 s2 List1, List2 Freq1, Freq2 v1, Sx1, n1, v2, Sx2, n2 Pooled 13-26 Inferential Statistics and Distributions Input p0 x n x1 x2 n1 n2 C.Level Description The expected sample proportion for 1.PropZTest. Must be a real number, such that 0 < p0 < 1. The count of successes in the sample for the 1.PropZTest and 1.PropZInt. Must be an integer , 0. The count of observations in the sample for the 1.PropZTest and 1.PropZInt. Must be an integer > 0. The count of successes from sample one for the 2.PropZTest and 2.PropZInt. Must be an integer , 0. The count of successes from sample two for the 2.PropZTest and 2.PropZInt. Must be an integer , 0. The count of observations in sample one for the 2.PropZTest and 2.PropZInt. Must be an integer > 0. The count of observations in sample two for the 2.PropZTest and 2.PropZInt. Must be an integer > 0. The confidence level for the interval instructions. Must be , 0 and <100. If it is , 1, it is assumed to be given as a percent and is divided by 100. Default=0.95. The matrix name that represents the columns and rows for the observed values of a two-way table of counts for the c2.Test. Observed must contain all integers , 0. Matrix dimensions must be at least 22. The matrix name that specifies where the expected values should be stored. Expected is created upon successful completion of the c2.Test. The names of the lists containing the data for LinRegTTest. Defaults are L1 and L2, respectively. The dimensions of Xlist and Ylist must be the same. The prompt for the name of the Y= variable where the calculated regression equation is to be stored. If a Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the RegEQ variable only. Observed (Matrix) Expected (Matrix) Xlist, Ylist RegEQ Inferential Statistics and Distributions 13-27 Test and Interval Output Variables The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press , 5 (5:Statistics), and then select the VARS menu listed in the last column below. Variables Tests p z , t, df v1, v2 Sx1, Sx2 c2, df v1, v2 Sx1, Sx2 n1, n2 SxP 1 2 lower, upper v Sx n v Sx n s a, b r r2 RegEQ SxP Intervals LinRegTTest, ANOVA p t, df VARS Menu TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST XY XY XY TEST EQ EQ EQ EQ p-value test statistics degrees of freedom sample mean of x values for sample 1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample n1, n2 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation SxP 1 2 13-28 Inferential Statistics and Distributions Distribution Functions DISTR menu To display the DISTR menu, press y [DISTR]. DISTR DRAW 1: normalpdf( 2: normalcdf( 3: invNorm( 4: tpdf( 5: tcdf( 6: c2pdf( 7: c2cdf 8: pdf( 9: cdf( 0: binompdf( A: binomcdf( B: poissonpdf( C: poissoncdf( D: geometpdf( E: geometcdf( Normal probability density Normal distribution probability Inverse cumulative normal distribution Student-t probability density Student-t distribution probability Chi-square probability density Chi-square distribution probability probability density distribution probability Binomial probability Binomial cumulative density Poisson probability Poisson cumulative density Geometric probability Geometric cumulative density Note: L199 and 199 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L199. normalpdf( norwmalpdf( computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste normalpdf( to the Y= editor. The probability density function (pdf) is: f ( x) = 1 2 e 2 - ( x - ) 2 2 , > 0 normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Ymin = 0 Ymax = .25 Tip: For plotting the normal distribution, you can set window variables Xmin and Xmax so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu. Inferential Statistics and Distributions 13-29 normalcdf( normalcdf( computes the normal distribution probability between lowerbound and upperbound for the specified mean m and standard deviation s. The defaults are m=0 and s=1. normalcdf(lowerbound,upperbound[,m,s]) invNorm( invNorm( computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s. It calculates the x value associated with an area to the left of the x value. 0 area 1 must be true. The defaults are m=0 and s=1. invNorm(area[,m,s]) tpdf( tpdf( computes the probability density function (pdf) for the Student-t distribution at a specified x value. df (degrees of freedom) must be >0. To plot the Student-t distribution, paste tpdf( to the Y= editor. The probability density function (pdf) is: f ( x) = [(df + 1) / 2] (df / 2) (1 + x 2 / df ) - ( df df + 1) / 2 tpdf(x,df) Note: For this example, Xmin = L4.5 Xmax = 4.5 Ymin = 0 Ymax = .4 13-30 Inferential Statistics and Distributions tcdf( tcdf( computes the Student-t distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be > 0. tcdf(lowerbound,upperbound,df) c2pdf( c2pdf( computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y= editor. The probability density function (pdf) is: f ( x) = 1 (1/2) df / 2 xdf / 2 - 1 e - x / 2 , x 0 (df / 2) c2pdf(x,df) Note: For this example, Xmin = 0 Xmax = 30 Ymin = L.02 Ymax = .132 c2cdf( c2cdf( computes the c2 (chi-square) distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be an integer > 0. c2cdf(lowerbound,upperbound,df) Inferential Statistics and Distributions 13-31 pdf( pdf( computes the probability density function (pdf) for the distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the distribution, paste pdf( to the Y= editor. The probability density function (pdf) is: f (x) = [( n + d) / 2 ] ( n / 2) (d / 2) n n / 2 n/ 2 - 1 x (1 + nx / d) - ( n + d ) / 2 , x 0 d where n = numerator degrees of freedom d = denominator degrees of freedom pdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1 cdf( cdf( computes the distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. numerator df and denominator df must be integers >0. cdf(lowerbound,upperbound,numerator df, denominator df) 13-32 Inferential Statistics and Distributions binompdf( binompdf( computes a probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be an integer or a list of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is: f ( x ) = n px(1 - p)n - x , x = 0,1, , n x where n = numtrials binompdf(numtrials,p[,x ]) binomcdf( binomcdf( computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of cumulative probabilities is returned. binomcdf(numtrials,p[,x ]) poissonpdf( poissonpdf( computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is: f ( x ) = e - x / x! , x = 0,1,2, poissonpdf(m,x ) Inferential Statistics and Distributions 13-33 poissoncdf( poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers. poissoncdf(m,x ) geometpdf( geometpdf( computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be an integer or a list of integers. The probability density function (pdf) is: f ( x ) = p(1 - p) x - 1 , x = 1,2, geometpdf(p,x ) geometcdf( geometcdf( computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be a real number or a list of real numbers. geometcdf(p,x ) 13-34 Inferential Statistics and Distributions Distribution Shading DISTR DRAW Menu To display the DISTR DRAW menu, press y [DISTR] ~. DISTR DRAW instructions draw various types of density functions, shade the area specified by lowerbound and upperbound, and display the computed area value. To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8). Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen. DISTR DRAW 1: ShadeNorm( 2:Shade_t( 3:Shadec2( 4:Shade( Shades normal distribution. Shades Student-t distribution. Shades c2 distribution. Shades distribution. Note: L199 and 199 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L199. ShadeNorm( ShadeNorm( draws the normal density function specified by mean m and standard deviation s and shades the area between lowerbound and upperbound. The defaults are m=0 and s=1. ShadeNorm(lowerbound,upperbound[,m,s]) Note: For this example, Xmin = 55 Xmax = 72 Ymin = L.05 Ymax = .2 Inferential Statistics and Distributions 13-35 Shade_t( Shade_t( draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shade_t(lowerbound,upperbound,df) Note: For this example, Xmin = L3 Xmax = 3 Ymin = L.15 Ymax = .5 Shadec2( Shadec2( draws the density function for the c2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shadec2(lowerbound,upperbound,df) Note: For this example, Xmin = 0 Xmax = 35 Ymin = L.025 Ymax = .1 Shade( Shade( draws the density function for the distribution specified by numerator df (degrees of freedom) and denominator df and shades the area between lowerbound and upperbound. Shade(lowerbound,upperbound,numerator df, denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = L.25 Ymax = .9 13-36 Inferential Statistics and Distributions 14 Contents Financial Functions Getting Started: Financing a Car ......................... 14-2 Getting Started: Computing Compound Interest.......... 14-3 Using the TVM Solver .................................... 14-4 Using the Financial Functions ........................... 14-5 Calculating Time Value of Money (TVM) ................. 14-6 Calculating Cash Flows .................................. 14-8 Calculating Amortization ................................ 14-9 Calculating Interest Conversion.......................... 14-12 Finding Days between Dates/Defining Payment Method ..... 14-13 Using the TVM Variables ................................. 14-14 Financial Functions 14-1 Getting Started: Financing a Car Getting Started is a fast-paced introduction. Read the chapter for details. You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? 1. Press z ~ ~ ~ to set the fixed-decimal mode setting to 2. The TI-83 will display all numbers with two decimal places. 2. Press y [FINANCE] to display the FINANCE CALC menu. 3. Press to select 1:TVM Solver. The TVM Solver is displayed. Press 48 to store 48 months to . Press 9000 to store 9,000 to PV. Press 250 to store L250 to PMT. (Negation indicates cash outflow.) Press 0 to store 0 to FV. Press 12 to store 12 payments per year to P/Y and 12 compounding periods per year to C/Y. Setting P/Y to 12 will compute an annual percentage rate (compounded monthly) for . Press to select PMT:END, which indicates that payments are due at the end of each period. 4. Press } } } } } } to move the cursor to the prompt. Press [SOLVE] to solve for . What APR should you look for? 14-2 Financial Functions Getting Started: Computing Compound Interest At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years? Note: Because there are no payments when you solve compound interest problems, PMT must be set to 0 and P/Y must be set to 1. 1. Press y [FINANCE] to display the FINANCE CALC menu. 2. Press to select 1:TVM Solver. Press 7 to enter the number of periods in years. Press 1250 to enter the present value as a cash outflow (investment). Press 0 to specify no payments. Press 2000 to enter the future value as a cash inflow (return). Press 1 to enter payment periods per year. Press 12 to set compounding periods per year to 12. 3. Press } } } } } to place the cursor on the prompt. 4. Press [SOLVE] to solve for , the annual interest rate. Financial Functions 14-3 Using the TVM Solver Using the TVM Solver The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable values, the TVM Solver solves for the fifth variable. The FINANCE VARS menu section (page 14.14) describes the five TVM variables (, , PV, PMT, and FV) and P/Y and C/Y. PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End (payment at the end of each period) and Pmt_Bgn (payment at the beginning of each period). To solve for an unknown TVM variable, follow these steps. 1. Press y [FINANCE] to display the TVM Solver. The screen below shows the default values with the fixeddecimal mode set to two decimal places. 2. Enter the known values for four TVM variables. Note: Enter cash inflows as positive numbers and cash outflows as negative numbers. 3. Enter a value for P/Y, which automatically enters the same value for C/Y; if P/Y C/Y, enter a unique value for C/Y. 4. Select END or BEGIN to specify the payment method. 5. Place the cursor on the TVM variable for which you want to solve. 6. Press [SOLVE]. The answer is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable. An indicator square in the left column designates the solution variable. 14-4 Financial Functions Using the Financial Functions Entering Cash Inflows and Cash Outflows When using the TI-83 financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-83 follows this convention when computing and displaying answers. To display the FINANCE CALC menu, press y [FINANCE]. CALC VARS 1: TVM Solver... 2: tvm_Pmt 3: tvm_ 4: tvm_PV 5: tvm_ 6: tvm_FV 7: npv( 8: irr( 9: bal( 0: GPrn( A: GInt( B: 4Nom( C: 4Eff( D: dbd( E: Pmt_End F: Pmt_Bgn FINANCE CALC Menu Displays the TVM Solver. Computes the amount of each payment. Computes the interest rate per year. Computes the present value. Computes the number of payment periods. Computes the future value. Computes the net present value. Computes the internal rate of return. Computes the amortization sched. balance. Computes the amort. sched. principal sum. Computes the amort. sched. interest sum. Computes the nominal interest rate. Computes the effective interest rate. Calculates the days between two dates. Selects ordinary annuity (end of period). Selects annuity due (beginning of period). Use these functions to set up and perform financial calculations on the home screen. TVM Solver TVM Solver displays the TVM Solver (page 14.4). Financial Functions 14-5 Calculating Time Value of Money (TVM) Calculating Time Value of Money Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the TVM variables (page 14.14). Note: To store a value to a TVM variable, use the TVM Solver (page 14.4) or use and any TVM variable on the FINANCE VARS menu (page 14.14). If you enter less than six arguments, the TI-83 substitutes a previously stored TVM variable value for each unspecified argument. If you enter any arguments with a TVM function, you must place the argument or arguments in parentheses. tvm_Pmt tvm_Pmt computes the amount of each payment. tvm_Pmt[(,,PV,FV,P/Y,C/Y)] Note: In the example above, the values are stored to the TVM variables in the TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount. 14-6 Financial Functions tvm_ tvm_ computes the annual interest rate. tvm_[(,PV,PMT,FV,P/Y,C/Y)] tvm_PV tvm_PV computes the present value. tvm_PV[(,,PMT,FV,P/Y,C/Y)] tvm_ tvm_ computes the number of payment periods. tvm_[(,PV,PMT,FV,P/Y,C/Y)] tvm_FV tvm_FV computes the future value. tvm_FV[(,,PV,PMT,P/Y,C/Y)] Financial Functions 14-7 Calculating Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for npv( and irr( use these arguments. interest rate is the rate by which to discount the cash flows (the cost of money) over one period. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. For example, express this uneven cash flow in lists. 2000 2000 2000 4000 4000 - 3000 CF0 = 2000 CFList = {2000,L3000,4000} CFFreq = {2,1,2} npv(, irr( npv( (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CF0,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero. irr(CF0,CFList[,CFFreq]) 1000 0 5000 3000 - 2000 - 2500 14-8 Financial Functions Calculating Amortization Calculating an Amortization Schedule bal( Use the amortization functions (menu items 9, 0, and A) to calculate balance, sum of principal, and sum of interest for an amortization schedule. bal( computes the balance for an amortization schedule using stored values for , PV, and PMT. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-83 uses the current Float/Fix decimal-mode setting. bal(npmt[,roundvalue]) GPrn(, GInt( GPrn( computes the sum of the principal during a specified period for an amortization schedule using stored values for , PV, and PMT. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify roundvalue, the TI-83 uses the current Float/Fix decimal-mode setting. Note: You must enter values for , PV, PMT, and before computing the principal. GPrn(pmt1,pmt2[,roundvalue]) GInt( computes the sum of the interest during a specified period for an amortization schedule using stored values for , PV, and PMT. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the interest; if you do not specify roundvalue, the TI-83 uses the current Float/Fix decimal-mode setting. GInt(pmt1,pmt2[,roundvalue]) Financial Functions 14-9 Amortization Example: Calculating an Outstanding Loan Balance You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table. 1. Press z. Press ~ ~ ~ to set the fixed-decimal mode setting to 2. Press ~ to select Par graphing mode. 2. Press y [FINANCE] to display the TVM Solver. 3. Press 360 to enter number of payments. Press 8 to enter the interest rate. Press 800 to enter the payment amount. Press 0 to enter the future value of the mortgage. Press 12 to enter the payments per year, which also sets the compounding periods per year to 12. Press to select PMT:END. 4. Press } } } } } to place the cursor on the PV prompt. Press [SOLVE] to solve for the present value. 5. Press o to display the parametric Y= editor. Turn off all stat plots. Press ,, to define X1T as T. Press y [FINANCE] 9 ,, to define Y1T as bal(T). 14-10 Financial Functions 6. Press p to display the window variables. Enter the values below. Tmin=0 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=50 Ymin=0 Ymax=125000 Yscl=10000 7. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press to view the balance at a specific time T. 8. Press y [TBLSET] and enter the values below. TblStart=0 @Tbl=12 9. Press y [TABLE] to display the table of outstanding balances (Y1T). 10.Press z ~ ~ to select G.T split-screen mode, in which the graph and table are displayed simultaneously. Press r to display X1T (time) and Y1T (balance) in the table. Financial Functions 14-11 Calculating Interest Conversion Calculating an Interest Conversion Use the interest conversion functions (menu items B and C) to convert interest rates from an annual effective rate to a nominal rate (4Nom( ) or from a nominal rate to an annual effective rate (4Eff( ). 4Nom( computes the nominal interest rate. effective rate and compounding periods must be real numbers. compounding periods must be >0. 4Nom(effective rate,compounding periods) 4Nom( 4Eff( 4Eff( computes the effective interest rate. nominal rate and compounding periods must be real numbers. compounding periods must be >0. 4Eff(nominal rate,compounding periods) 14-12 Financial Functions Finding Days between Dates/Defining Payment Method dbd( Use the date function dbd( (menu item D) to calculate the number of days between two dates using the actual-daycount method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. Note: Dates must be between the years 1950 through 2049. dbd(date1,date2) You can enter date1 and date2 in either of two formats. MM.DDYY (United States) DDMM.YY (Europe) The decimal placement differentiates the date formats. Defining the Payment Method Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the TVM Solver is updated. Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category. Pmt_End is the default. Pmt_End Pmt_End On the TVM Solver's PMT:END BEGIN line, select END to set PMT to ordinary annuity. Pmt_Bgn Pmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category. Pmt_Bgn On the TVM Solver's PMT:END BEGIN line, select BEGIN to set PMT to annuity due. Financial Functions 14-13 Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu, press y [FINANCE] ~. You can use TVM variables in TVM functions and store values to them on the home screen. CALC VARS 1: 2: 3: PV 4: PMT 5: FV 6: P/Y 7: C/Y Total number of payment periods Annual interest rate Present value Payment amount Future value Number of payment periods per year Number of compounding periods/year , , PV, PMT, FV , , PV, PMT, and FV are the five TVM variables. They represent the elements of common financial transactions, as described in the table above. is an annual interest rate that is converted to a per-period rate based on the values of P/Y and C/Y. P/Y is the number of payment periods per year in a financial transaction. C/Y is the number of compounding periods per year in the same transaction. P/Y and C/Y When you store a value to P/Y, the value for C/Y automatically changes to the same value. To store a unique value to C/Y, you must store the value to C/Y after you have stored a value to P/Y. 14-14 Financial Functions 15 Contents CATALOG, Strings, Hyperbolic Functions Browsing the TI-83 CATALOG ........................... 15-2 Entering and Using Strings ............................... 15-3 Storing Strings to String Variables ....................... 15-4 String Functions and Instructions in the CATALOG ...... 15-6 Hyperbolic Functions in the CATALOG .................. 15-10 CATALOG, Strings, Hyperbolic Functions 15-1 Browsing the TI-83 CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-83. You also can access each CATALOG item from a menu or the keyboard, except: The six string functions (page 15.6) The six hyperbolic functions (page 15.10) The solve( instruction without the equation solver editor (Chapter 2) The inferential stat functions without the inferential stat editors (Chapter 13) Note: The only CATALOG programming commands you can execute from the home screen are GetCalc(, Get(, and Send(. Selecting an Item from the CATALOG To select a CATALOG item, follow these steps. 1. Press y CATALOG to display the CATALOG. The 4 in the first column is the selection cursor. 2. Press or } to scroll the CATALOG until the selection cursor points to the item you want. To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on. Items that begin with a number are in alphabetical order according to the first letter after the number. For example, 2.PropZTest( is among the items that begin with the letter P. Functions that appear as symbols, such as +, L1, <, and (, follow the last item that begins with Z. To jump to the first symbol, !, press [q]. 3. Press to paste the item to the current screen. Tip: From the top of the CATALOG menu, press } to move to the bottom. From the bottom, press to move to the top. 15-2 CATALOG, Strings, Hyperbolic Functions Entering and Using Strings What Is a String? A string is a sequence of characters that you enclose within quotation marks. On the TI-83, a string has two primary applications. It defines text to be displayed in a program. It accepts input from the keyboard in a program. Characters are the units that you combine to form a string. Count each number, letter, and space as one character. Count each instruction or function name, such as sin( or cos(, as one character; the TI-83 interprets each instruction or function name as one character. Entering a String To enter a string on a blank line on the home screen or in a program, follow these steps. 1. Press to indicate the beginning of the string. 2. Enter the characters that comprise the string. Use any combination of numbers, letters, function names, or instruction names to create the string. To enter a blank space, press [']. To enter several alpha characters in a row, press y [A.LOCK] to activate alpha-lock. 3. Press to indicate the end of the string. "string" 4. Press . On the home screen, the string is displayed on the next line without quotations. An ellipsis (...) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and |. Note: Quotation marks do not count as string characters. CATALOG, Strings, Hyperbolic Functions 15-3 Storing Strings to String Variables String Variables The TI-83 has 10 variables to which you can store strings. You can use string variables with string functions and instructions. To display the VARS STRING menu, follow these steps. 1. Press to display the VARS menu. Move the cursor to 7:String. 2. Press to display the STRING secondary menu. 15-4 CATALOG, Strings, Hyperbolic Functions Storing a String to a String Variable To store a string to a string variable, follow these steps. 1. Press , enter the string, and press . 2. Press . 3. Press 7 to display the VARS STRING menu. 4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the string. The string variable is pasted to the current cursor location, next to the store symbol (!). 5. Press to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks. Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable from the VARS STRING menu, and then press . The string is displayed. CATALOG, Strings, Hyperbolic Functions 15-5 String Functions and Instructions in the CATALOG Displaying String Functions and Instructions in the CATALOG String functions and instructions are available only from the CATALOG. The table below lists the string functions and instructions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... Equ4String( expr( ... inString( ... length( ... String4Equ( sub( ... Converts an equation to a string. Converts a string to an expression. Returns a character's place number. Returns a string's character length. Converts a string to an equation. Returns a string subset as a string. + (Concatenation) To concatenate two or more strings, follow these steps. 1. Enter string1, which can be a string or string name. 2. Press . 3. Enter string2, which can be a string or string name. If necessary, press and enter string3, and so on. string1+string2+string3. . . 4. Press to display the strings as a single string. Selecting a String To select a string function or instruction and paste it to the current screen, follow the steps on page 15.2. Function from the CATALOG 15-6 CATALOG, Strings, Hyperbolic Functions Equ4String( Equ4String( converts to a string an equation that is stored to any VARS Y.VARS variable. Yn contains the equation. Strn (from Str1 to Str9, or Str0) is the string variable to which you want the equation to be stored as a string. Equ4String(Yn,Strn) expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable. expr(string) inString( inString( returns the character position in string of the first character of substring. string can be a string or a string variable. start is an optional character position at which to start the search; the default is 1. inString(string,substring[,start]) Note: If string does not contain substring, or start is greater than the length of string, inString( returns 0. CATALOG, Strings, Hyperbolic Functions 15-7 length( length( returns the number of characters in string. string can be a string or string variable. Note: An instruction or function name, such as sin( or cos(, counts as one character. length(string) String4Equ( String4Equ( converts string into an equation and stores the equation to Yn. string can be a string or string variable. String4Equ( is the inverse of Equ4String(. String4Equ(string,Yn) 15-8 CATALOG, Strings, Hyperbolic Functions sub( sub( returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset. sub(string,begin,length) Entering a Function to Graph during Program Execution In a program, you can enter a function to graph during program execution using these commands. Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt. CATALOG, Strings, Hyperbolic Functions 15-9 Hyperbolic Functions in the CATALOG Hyperbolic Functions The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... cosh( cosh L1( ... sinh( sinh L1( ... tanh( tanh L1( ... Hyperbolic cosine Hyperbolic arccosine Hyperbolic sine Hyperbolic arcsine Hyperbolic tangent Hyperbolic arctangent sinh(, cosh(, tanh( sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers, expressions, and lists. sinh(value) cosh(value) tanh(value) sinhL1(, coshL1(, tanhL1( sinhL1( is the hyperbolic arcsine function. coshL1( is the hyperbolic arccosine function. tanhL1( is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists. sinhL1(value) coshL1(value) sinhL1(value) 15-10 CATALOG, Strings, Hyperbolic Functions 16 Contents Programming Getting Started: Volume of a Cylinder .................... 16-2 Creating and Deleting Programs ......................... 16-4 Entering Command Lines and Executing Programs ...... 16-5 Editing Programs ........................................ 16-6 Copying and Renaming Programs ........................ 16-7 PRGM CTL (Control) Instructions ....................... 16-8 PRGM I/O (Input/Output) Instructions ................... 16-16 Calling Other Programs as Subroutines .................. 16-22 Programming 16-1 Getting Started: Volume of a Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-83 executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume. 1. Press ~ ~ to display the PRGM NEW menu. 2. Press to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on. Press [C] [Y] [L] [I] [N] [D] [E] [R], and then press to name the program CYLINDER. You are now in the program editor. The colon ( : ) in the first column of the second line indicates the beginning of a command line. 3. Press ~ 2 to select 2:Prompt from the PRGM I/O menu. Prompt is copied to the command line. Press [R] [H] to enter the variable names for radius and height. Press . 4. Press y p [R] [H] [V] to enter the expression pR2H and store it to the variable V. 16-2 Programming 5. Press ~ 3 to select 3:Disp from the PRGM I/O menu. Disp is pasted to the command line. Press y [A.LOCK] [V] [O] [L] [U] [M] [E]['] [I] [S] [V] to set up the program to display the text VOLUME IS on one line and the calculated value of V on the next. 6. Press y [QUIT] to display the home screen. 7. Press to display the PRGM EXEC menu. The items on this menu are the names of stored programs. 8. Press to paste prgmCYLINDER to the current cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDER before you press .) 9. Press to execute the program. Enter 1.5 for the radius, and then press . Enter 3 for the height, and then press . The text VOLUME IS, the value of V, and Done are displayed. Repeat steps 7 through 9 and enter different values for R and H. Programming 16-3 Creating and Deleting Programs What Is a Program? A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI-83 performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-83 can store is limited only by available memory. To create a new program, follow these steps. 1. Press | to display the PRGM NEW menu. Creating a New Program 2. Press to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on. 3. Press a letter from A to Z or q to enter the first character of the new program name. Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 4. Enter zero to seven letters, numbers, or q to complete the new program name. 5. Press . The program editor is displayed. 6. Enter one or more program commands (page 16.5). 7. Press y [QUIT] to leave the program editor and return to the home screen. Managing Memory and Deleting a Program To check whether adequate memory is available for a program you want to enter, press y [MEM], and then select 1:Check RAM from the MEMORY menu (Chapter 18). To increase available memory, press y [MEM], and then select 2:Delete from the MEMORY menu (Chapter 18). To delete a specific program, press y [MEM], select 2:Delete from the MEMORY menu, and then select 7:Prgm from the DELETE FROM secondary menu (Chapter 18). 16-4 Programming Entering Command Lines and Executing Programs Entering a Program Command Line You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon. Note: A command line can be longer than the screen is wide; long command lines wrap to the next screen line. While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways. Select a menu item, which pastes the item to the current command line. Press `. When you complete a command line, press . The cursor moves to the next command line. Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution. You can call another program as a subroutine (page 16.15 and page 16.22). Executing a Program To execute a program, begin on a blank line on the home screen and follow these steps. 1. Press to display the PRGM EXEC menu. 2. Select a program name from the PRGM EXEC menu (page 16.7). prgmname is pasted to the home screen (for example, prgmCYLINDER). 3. Press to execute the program. While the program is executing, the busy indicator is on. Last Answer (Ans) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1). The TI-83 checks for errors during program execution. It does not check for errors as you enter a program. Breaking a Program To stop program execution, press . The ERR:BREAK menu is displayed. To return to the home screen, select 1:Quit. To go where the interruption occurred, select 2:Goto. Programming 16-5 Editing Programs Editing a Program To edit a stored program, follow these steps. 1. Press ~ to display the PRGM EDIT menu. 2. Select a program name from the PRGM EDIT menu (page 16.7). Up to the first seven lines of the program are displayed. Note: The program editor does not display a $ to indicate that a program continues beyond the screen. 3. Edit the program command lines. Move the cursor to the appropriate location, and then delete, overwrite, or insert. Press ` to clear all program commands on the command line (the leading colon remains), and then enter a new program command. Tip: To move the cursor to the beginning of a command line, press y |; to move to the end, press y ~. To scroll the cursor down seven command lines, press . To scroll the cursor up seven command lines, press }. Inserting and Deleting Command Lines To insert a new command line anywhere in the program, place the cursor where you want the new line, press y [INS], and then press . A colon indicates a new line. To delete a command line, place the cursor on the line, press ` to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon. 16-6 Programming Copying and Renaming Programs Copying and Renaming a Program To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program (page 16.4), and then follow these steps. 1. Press y [RCL]. Rcl is displayed on the bottom line of the program editor in the new program (Chapter 1). 2. Press | to display the PRGM EXEC menu. 3. Select a name from the menu. prgmname is pasted to the bottom line of the program editor. 4. Press . All command lines from the selected program are copied into the new program. Copying programs has at least two convenient applications. You can create a template for groups of instructions that you use frequently. You can rename a program by copying its contents into a new program. Note: You also can copy all the command lines from one existing program to another existing program using RCL. Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-83 sorts PRGM EXEC and PRGM EDIT menu items automatically into alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0. To jump to the first program name that begins with a particular alpha character or q, press [letter from A to Z or q]. Tip: From the top of either the PRGM EXEC or PRGM EDIT menu, press } to move to the bottom. From the bottom, press to move to the top. To scroll the cursor down the menu seven items, press . To scroll the cursor up the menu seven items, press }. Programming 16-7 PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL I/O EXEC 1: If 2: Then 3: Else 4: For( 5: While 6: Repeat 7: End 8: Pause 9: Lbl 0: Goto A: IS>( B: DS<( C: Menu( D: prgm E: Return F: Stop G: DelVar H: GraphStyle( Creates a conditional test. Executes commands when If is true. Executes commands when If is false. Creates an incrementing loop. Creates a conditional loop. Creates a conditional loop. Signifies the end of a block. Pauses program execution. Defines a label. Goes to a label. Increments and skips if greater than. Decrements and skips if less than. Defines menu items and branches. Executes a program as a subroutine. Returns from a subroutine. Stops execution. Deletes a variable from within program. Designates the graph style to be drawn. These menu items direct the flow of an executing program. They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program. To return to the program editor without selecting an item, press `. Controlling Program Flow Program control instructions tell the TI-83 which command to execute next in a program. If, While, and Repeat check a defined condition to determine which command to execute next. Conditions frequently use relational or Boolean tests (Chapter 2), as in: If A<7:A+1!A or If N=1 and M=1:Goto Z 16-8 Programming If Use If for testing and branching. If condition is false (zero), then the command immediately following If is skipped. If condition is true (nonzero), then the next command is executed. If instructions can be nested. :If condition :command (if true) :command Program Output If.Then Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group of commands. :If condition :Then :command (if true) :command (if true) :End :command Program Output Programming 16-9 If-Then-Else Else following If.Then executes a group of commands if condition is false (zero). End identifies the end of the group of commands. :If condition :Then :command (if true) :command (if true) :Else :command (if false) :command (if false) :End :command Program Output For( For( loops and increments. It increments variable from begin to end by increment. increment is optional (default is 1) and can be negative (end<begin). end is a maximum or minimum value not to be exceeded. End identifies the end of the loop. For( loops can be nested. :For(variable,begin,end[,increment]) :command (while end not exceeded) :command (while end not exceeded) :End :command Program Output 16-10 Programming While While performs a group of commands while condition is true. condition is frequently a relational test (Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the program executes a group of commands. End signifies the end of the group. When condition is false (zero), the program executes each command following End. While instructions can be nested. :While condition :command (while condition is true) :command (while condition is true) :End :command Program Output Repeat Repeat repeats a group of commands until condition is true (nonzero). It is similar to While, but condition is tested when End is encountered; therefore, the group of commands is always executed at least once. Repeat instructions can be nested. :Repeat condition :command (until condition is true) :command (until condition is true) :End :command Program Output Programming 16-11 End End identifies the end of a group of commands. You must include an End instruction at the end of each For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If.Then group and each If.Then.Else group. Pause suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press to resume execution. Pause Pause without a value temporarily pauses the program. If the DispGraph or Disp instruction has been executed, the appropriate screen is displayed. Pause with value displays value on the current home screen. value can be scrolled. Pause [value] Program Output 16-12 Programming Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or q). Lbl label Goto causes the program to branch to label when Goto is encountered. Goto label Program Output IS>( IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed. variable cannot be a system variable. :IS>(variable,value) :command (if answer value) :command (if answer > value) Program Output Note: IS>( is not a looping instruction. Programming 16-13 DS<( DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable. :DS<(variable,value) :command (if answer , value) :command (if answer < value) Program Output Note: DS<( is not a looping instruction. Menu( Menu( sets up branching within a program. If Menu( is encountered during program execution, the menu screen is displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item. The menu title is enclosed in quotation marks ( " ). Up to seven pairs of menu items follow. Each pair comprises a text item (also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection. Menu("title","text1",label1,"text2",label2, . . .) Program Output The program above pauses until you select 1 or 2. If you select 2, for example, the menu disappears and the program continues execution at Lbl B. 16-14 Programming prgm Use prgm to execute other programs as subroutines (page 16.22). When you select prgm, it is pasted to the cursor location. Enter characters to spell a program name. Using prgm is equivalent to selecting existing programs from the PRGM EXEC menu; however, it allows you to enter the name of a program that you have not yet created. prgmname Note: You cannot directly enter the subroutine name when using RCL. You must paste the name from the PRGM EXEC menu (page 16.7). Return Return quits the subroutine and returns execution to the calling program (page 16.22), even if encountered within nested loops. Any loops are ended. An implied Return exists at the end of any program that is called as a subroutine. Within the main program, Return stops execution and returns to the home screen. Stop Stop stops execution of a program and returns to the home screen. Stop is optional at the end of a program. DelVar deletes from memory the contents of variable. DelVar variable DelVar GraphStyle( GraphStyle( designates the style of the graph to be drawn. function# is the number of the Y= function name in the current graphing mode. graphstyle is a number from 1 to 7 that corresponds to the graph style, as shown below. 1 = (line) 2 = (thick) 3 = (shade above) 4 = (shade below) 5 = (path) 6 = (animate) 7 = (dot) GraphStyle(function#,graphstyle) For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to (path; 5). Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3. Programming 16-15 PRGM I/O (Input/Output) Instructions PRGM I/O Menu To display the PRGM I/O (program input/output) menu, press ~ from within the program editor only. CTL I/O EXEC 1: Input 2: Prompt 3: Disp 4: DispGraph 5: DispTable 6: Output( 7: getKey 8: ClrHome 9: ClrTable 0: GetCalc( A: Get( B: Send( Enters a value or uses the cursor. Prompts for entry of variable values. Displays text, value, or the home screen. Displays the current graph. Displays the current table. Displays text at a specified position. Checks the keyboard for a keystroke. Clears the display. Clears the current table. Gets a variable from another TI-83. Gets a variable from CBL 2/CBL or CBR. Sends a variable to CBL 2/CBL or CBR. These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution. To return to the program editor without selecting an item, press `. Displaying a Graph with Input Input without a variable displays the current graph. You can move the free-moving cursor, which updates X and Y (and R and q for PolarGC format). The pause indicator is on. Press to resume program execution. Input Program Output 16-16 Programming Storing a Variable Value with Input Input with variable displays a ? (question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press . The value is evaluated and stored to variable, and the program resumes execution. Input [variable] You can display text or the contents of Strn (a string variable) of up to 16 characters as a prompt. During program execution, enter a value after the prompt and then press . The value is stored to variable, and the program resumes execution. Input ["text",variable] Input [Strn,variable] Program Output Note: When a program prompts for input of lists and Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks ( " ) around the expressions. Programming 16-17 Prompt During program execution, Prompt displays each variable, one at a time, followed by =?. At each prompt, enter a value or expression for each variable, and then press . The values are stored, and the program resumes execution. Prompt variableA[,variableB,...,variable n] Program Output Note: Y= functions are not valid with Prompt. Displaying the Home Screen Disp (display) without a value displays the home screen. To view the home screen during program execution, follow the Disp instruction with a Pause instruction. Disp Displaying Values and Messages Disp with one or more values displays the value of each. Disp [valueA,valueB,valueC,...,value n] If value is a variable, the current value is displayed. If value is an expression, it is evaluated and the result is displayed on the right side of the next line. If value is text within quotation marks, it is displayed on the left side of the current display line. ! is not valid as text. Program Output If Pause is encountered after Disp, the program halts temporarily so you can examine the screen. To resume execution, press . Note: If a matrix or list is too large to display in its entirety, ellipses (...) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use Pause value (page 16.12). 16-18 Programming DispGraph DispGraph (display graph) displays the current graph. If Pause is encountered after DispGraph, the program halts temporarily so you can examine the screen. Press to resume execution. DispTable DispTable (display table) displays the current table. The program halts temporarily so you can examine the screen. Press to resume execution. Output( Output( displays text or value on the current home screen beginning at row (1 through 8) and column (1 through 16), overwriting any existing characters. Tip: You may want to precede Output( with ClrHome (page 16.20). Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entry format and wrap to the next line. ! is not valid as text. Output(row,column,"text") Output(row,column,value) Program Output For Output( on a Horiz split screen, the maximum value for row is 4. Programming 16-19 getKey getKey returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control, for example, when creating video games. Program Output Note: , , , and were pressed during program execution. Note: You can press at any time during execution to break the program (page 16.5). TI-83 Key Code Diagram ClrHome, ClrTable ClrHome (clear home screen) clears the home screen during program execution. ClrTable (clear table) clears the values in the table during program execution. 16-20 Programming GetCalc( GetCalc( gets the contents of variable on another TI-83 and stores it to variable on the receiving TI-83. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. GetCalc(variable) Note: GetCalc( does not work between TI.82s and TI-83s. Get(, Send( Get( gets data from the Calculator-Based Laboratory (CBL 2, CBL) System or Calculator-Based Ranger (CBR) and stores it to variable on the receiving TI-83. variable can be a real number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. Get(variable) Note: If you transfer a program that references the Get( command to the TI-83 from a TI.82, the TI-83 will interpret it as the Get( described above. Use GetCalc( to get data from another TI-83. Send( sends the contents of variable to the CBL 2/CBL or CBR. You cannot use it to send to another TI-83. variable can be a real number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. variable can be a list of elements. Send(variable) Note: This program gets sound data and time in seconds from CBL 2/CBL. Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from the home screen (Chapter 15). Programming 16-21 Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-83, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself. You can enter a program name on a command line in either of two ways. Press | to display the PRGM EXEC menu and select the name of the program (page 16.7). prgmname is pasted to the current cursor location on a command line. Select prgm from the PRGM CTL menu, and then enter the program name (page 16.15). prgmname When prgmname is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent command in the first program when it encounters either Return or the implied Return at the end of the second program. Program Output & Subroutine ( ' Notes about Calling Programs Variables are global. label used with Goto and Lbl is local to the program where it is located. label in one program is not recognized by another program. You cannot use Goto to branch to a label in another program. Return exits a subroutine and returns to the calling program, even if it is encountered within nested loops. 16-22 Programming 17 Contents Applications Comparing Test Results Using Box Plots ................ 17-2 Graphing Piecewise Functions ........................... 17-4 Graphing Inequalities .................................... 17-5 Solving a System of Nonlinear Equations ................ 17-6 Using a Program to Create the Sierpinski Triangle ....... 17-7 Graphing Cobweb Attractors ............................ 17-8 Using a Program to Guess the Coefficients ............... 17-9 Graphing the Unit Circle and Trigonometric Curves...... 17-10 Finding the Area between Curves ........................ 17-11 Using Parametric Equations: Ferris Wheel Problem ...... 17-12 Demonstrating the Fundamental Theorem of Calculus ... 17-14 Computing Areas of Regular N-Sided Polygons .......... 17-16 Computing and Graphing Mortgage Payments ........... 17-18 Applications 17-1 Comparing Test Results Using Box Plots Problem An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women. The test involved 30 small objects, which participants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other 15 objects one by one in their right hands and guessed what they were. Use box plots to compare visually the correct-guess data from this table. Correct Guesses Women Left 8 9 12 11 10 8 12 7 9 11 Women Right 4 1 8 12 11 11 13 12 11 12 Men Left 7 8 7 5 7 8 11 4 10 14 13 5 Men Right 12 6 12 12 7 11 12 8 12 11 9 9 Procedure 1. Press ... 5 to select 5:SetUpEditor. Enter list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by commas. Press . The stat list editor now contains only these four lists. 2. Press ... 1 to select 1:Edit. 3. Enter into WLEFT the number of correct guesses each woman made using her left hand (Women Left). Press ~ to move to WRGHT and enter the number of correct guesses each woman made using her right hand (Women Right). 4. Likewise, enter each man's correct guesses in MLEFT (Men Left) and MRGHT (Men Right). 5. Press y [STAT PLOT]. Select 1:Plot1. Turn on plot 1; define it as a modified box plot that uses WLEFT. Move the cursor to the top line and select Plot2. Turn on plot 2; define it as a modified box plot that uses WRGHT. 17-2 Applications 6. Press o. Turn off all functions. 7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women's results. 8. Press r. % Women's left-hand data % Women's right-hand data Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the outlier to the women's righthand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots? 9. Examine the men's results. Redefine plot 1 to use MLEFT, redefine plot 2 to use MRGHT. Press r. % Men's left-hand data % Men's right-hand data Press | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. What difference do you see between the plots? 10.Compare the left-hand results. Redefine plot 1 to use WLEFT, redefine plot 2 to use MLEFT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better left-hand guessers, men or women? 11.Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use MRGHT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better right-hand guessers? In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough? Applications 17-3 Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket. The fine (Y) as a function of kilometers per hour (X) is: Y=0 Y = 50 + 5 (X N 45) Y = 50 + 5 ... 10 + 10 (X N 55) Y = 50 + 5 ... 10 + 10 ... 10 + 20 (X N 65) 0 < X 45 45 < X 55 55 < X 65 65 < X Procedure 1. Press z. Select Func and the default settings. 2. Press o. Turn off all functions and stat plots. Enter the Y= function to describe the fine. Use the TEST menu operations to define the piecewise function. Set the graph style for Y1 to (dot). 3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore Xmax and Ymax; they are set by @X and @Y in step 4. 4. Press y [QUIT] to return to the home screen. Store 1 to @X, and then store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for @X and @Y produce nice values for tracing. 5. Press r to plot the function. At what speed does the ticket exceed 250? 17-4 Applications Graphing Inequalities Problem Graph the inequality 0.4X 3 N 3X + 5 < 0.2X + 4. Use the TEST menu operations to explore the values of X where the inequality is true and where it is false. 1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons to (dot) in the Y= editor. 2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5. Procedure 3. Enter the statement of the inequality as Y6. This function evaluates to 1 if true or 0 if false. 4. Press q 6 to graph the inequality in the standard window. 5. Press r to move to Y6. Then press | and ~ to trace the inequality, observing the value of Y. 6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality. 7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false. Applications 17-5 Solving a System of Nonlinear Equations Problem Using a graph, solve the equation X3 N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X 3N2X and Y = 2cos(X). Use ZOOM factors to control the decimal places displayed on the graph. 1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions. Procedure 2. Press q 4 to select 4:ZDecimal. The display shows that two solutions may exist (points where the two functions appear to intersect). 3. Press q ~ 4 to select 4:SetFactors from the ZOOM MEMORY menu. Set XFact=10 and YFact=10. 4. Press q 2 to select 2:Zoom In. Use |, ~, }, and to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the X and Y values have one decimal place. 5. Press to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the X and Y values have two decimal places. 6. Press to zoom in again. Move the free-moving cursor onto a point exactly on the intersection. Notice the number of decimal places. 7. Press y [CALC] 5 to select 5:intersect. Press to select the first curve and to select the second curve. To guess, move the trace cursor near the intersection. Press . What are the coordinates of the intersection point? 8. Press q 4 to select 4:ZDecimal to redisplay the original graph. 9. Press q. Select 2:Zoom In and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display. 17-6 Applications Using a Program to Create the Sierpinski Triangle Setting up the Program This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press . The program editor is displayed. PROGRAM:SIERPINS :FnOff :ClrDraw :PlotsOff :AxesOff :0!Xmin:1!Xmax :0!Ymin:1!Ymax :rand!X:rand!Y :For(K,1,3000) :rand!N :If N1 3 :Then :.5X!X :.5Y!Y :End :If 1 3 <N and N2 3 :Then :.5(.5+X)!X :.5(1+Y)!Y :End :If 2 3 <N :Then :.5(1+X)!X :.5Y!Y :End :Pt-On(X,Y) :End :StorePic 6 Program Set viewing window. Beginning of For group. If/Then group If/Then group. If/Then group. Draw point. End of For group. Store picture. After you execute the program above, you can recall and display the picture with the instruction RecallPic 6. Applications 17-7 Graphing Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. 1. Press z. Select Seq and the default mode settings. Press y [FORMAT]. Select Web format and the default format settings. 2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01 Procedure 3. Press y [QUIT] to return to the home screen, and then store 2.9 to K. 4. Press p. Set the window variables. nMin=0 nMax=10 PlotStart=1 PlotStep=1 Xmin=0 Xmax=1 Xscl=1 Ymin=M.26 Ymax=1.1 Yscl=1 5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor. 6. Change K to 3.44 and trace the graph to show a cobweb with two attractors. 7. Change K to 3.54 and trace the graph to show a cobweb with four attractors. 17-8 Applications Using a Program to Guess the Coefficients Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct. PROGRAM:GUESS :PlotsOff :Func :FnOff :Radian :ClrHome :"Asin(BX)"!Y1 :"Csin(DX)"!Y2 :GraphStyle(1,1) :GraphStyle(2,5) :FnOff 2 :randInt(1,10)!A :randInt(1,10)!B :0!C:0!D :L2p!Xmin :2p!Xmax :p2!Xscl :L10!Ymin :10!Ymax :1!Yscl :DispGraph :Pause :FnOn 2 :Lbl Z :Prompt C,D :DispGraph :Pause :If C=A :Text(1,1,"C IS OK") :If CA :Text(1,1,"C IS WRONG") :If D=B :Text(1,50,"D IS OK") :If DB :Text(1,50,"D IS WRONG") :DispGraph :Pause :If C=A and D=B :Stop :Goto Z Program Define equations. Set line and path graph styles. Initialize coefficients. Set viewing window. Display graph. Prompt for guess. Display graph. Display results. Display graph. Quit if guesses are correct. Applications 17-9 Graphing the Unit Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). Procedure 1. Press z. Select Par, Simul, and the default settings. 2. Press p. Set the viewing window. Tmin=0 Tmax=2p Tstep=.1 Xmin=L2 Xmax=7.4 Xscl=p2 Ymin=L3 Ymax=3 Yscl=1 3. Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0). 4. Enter the expressions to define the sine curve. 5. Press r. As the graph is plotting, you may press to pause and again to resume graphing as you watch the sine function "unwrap" from the unit circle. Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig function to unwrap that function. 17-10 Applications Finding the Area between Curves Problem Find the area of the region bounded by f(x) g(x) x = 300x / ( x2 + 625) = 3cos(.1x) = 75 Procedure 1. Press z. Select the default mode settings. 2. Press p. Set the viewing window. Xmin=0 Xmax=100 Xscl=10 Ymin=L5 Ymax=10 Yscl=1 Xres=1 3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300X(X2+625) Y2=3cos(.1X) 4. Press y [CALC] 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X. 5. Press y [QUIT] to go to the home screen. Press y [DRAW] 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75) 6. Press y [QUIT] to return to the home screen. Enter the expression to evaluate the integral for the shaded region. fnInt(Y1Y2,X,Ans,75) The area is 325.839962. Applications 17-11 Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds. The parametric equations below describe the location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferris wheel, and (10,10) is the passenger's location at the rightmost point, when T=0. X(T) = r cos a Y(T) = r + r sin a where a = 2pTs and r = d 2 A person standing on the ground throws a ball to the ferris wheel passenger. The thrower's arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel's lowest point (25,0). The person throws the ball with velocity (v0) of 22 meters per second at an angle (q) of 66 from the horizontal. The parametric equations below describe the location of the ball at time T. X(T) = b N Tv 0 cosq Y(T) = Tv 0 sinq N (g 2 ) T 2 9.8 m / sec2 Procedure where g= 1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode simulates the two objects in motion over time. 2. Press p. Set the viewing window. Tmin=0 Tmax=12 Tstep=.1 Xmin=L13 Xmax=34 Xscl=10 Ymin=0 Ymax=31 Yscl=10 3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for X2T to (path). Tip: Try setting the graph styles to X1T and X2T, which simulates a chair on the ferris wheel and the ball flying through the air when you press s. 17-12 Applications 4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. 5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Tmax=3 Tstep=.03 Xmin=0 Xmax=23.5 Xscl=10 Ymin=10 Ymax=25.5 Yscl=10 6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of X, Y, and T. 7. Press to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first? You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion. Applications 17-13 Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: F(x) = Dx 1 x 1t dt = ln(x), x > 0 and that [1 x 1t dt = 1x Procedure 1 1. Press z. Select the default settings. 2. Press p. Set the viewing window. Xmin=.01 Xmax=10 Xscl=1 Ymin=M1.5 Ymax=2.5 Yscl=1 Xres=3 3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1T from 1 to X and the function ln(X). Set the graph style for Y1 to (line) and Y2 to (path). 4. Press r. Press |, }, ~, and to compare the values of Y1 and Y2. 5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1X and the function 1X. Set the graph style for Y3 to (line) and Y4 to (thick). 6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Y3 and Y4. 17-14 Applications Problem 2 Explore the functions defined by y= 2 M x t2 dt, 0 x t 2 dt, and 2 x t2 dt Procedure 2 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5. 2. Press q 6 to select 6:ZStandard. 3. Press r. Notice that the functions appear identical, only shifted vertically by a constant. 4. Press o. Enter the numerical derivative of Y5 in Y6. 5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative. Applications 17-15 Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr2. Consider the formula A = NB 2 sin(pN) cos(pN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex. N = 4 sides N = 8 sides N = 12 sides Procedure 1. Press 0 to select 0:Solver from the MATH menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press } to display the equation editor. 2. Enter the formula as 0=ANNB2sin(p / N)cos(p / N), and then press . The interactive solver editor is displayed. 3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters. 4. Press } } to move the cursor onto A, and then press [SOLVE]. The solution for A is displayed on the interactive solver editor. 5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6. To find the distance B, move the cursor onto B, and then press [SOLVE]. 6. Enter N=8. To find the distance B, move the cursor onto B, and then press [SOLVE]. Find B for N=9, and then for N=10. 17-16 Applications Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with p62 (the area of a circle with radius 6), which is approximately 113.097. 7. Enter B=6. To find the area A, move the cursor onto A, and then press [SOLVE]. Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice that as N gets large, the area A approaches pB2. Now graph the equation to see visually how the area changes as the number of sides gets large. 8. Press z. Select the default mode settings. 9. Press p. Set the viewing window. Xmin=0 Xmax=200 Xscl=10 Ymin=0 Ymax=150 Yscl=10 Xres=1 10.Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X in place of N. Set the graph styles as shown. 11.Press r. After the graph is plotted, press 100 to trace to X=100. Press 150 . Press 188 . Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large. Applications 17-17 Computing and Graphing Mortgage Payments Problem You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. 1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. 2. Press y [FINANCE] 1 to display the TVM Solver. Enter these values. Procedure Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter 0 for FV, since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period. 3. Move the cursor onto the PV= prompt, and then press [SOLVE]. The present value, or mortgage amount, of the house is displayed at the PV= prompt. 17-18 Applications Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. 4. Press z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. Note: GPrn( and GInt( are located on the FINANCE CALC menu. 6. Press p. Set these window variables. Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin=0 Ymax=1000 Yscl=100 Tip: To increase the graph speed, change Tstep to 24. 7. Press r. After the graph is drawn, press 240 to move the trace cursor to T=240, which is equivalent to 20 years of payments. The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800. Applications 17-19 8. Press to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y [QUIT] y [FINANCE] 9 to paste 9:bal( to the home screen. Check the figures from the graph. At which monthly payment will the principal allocation surpass the interest allocation? 17-20 Applications 18 Contents Memory Management 18-2 18-3 18-4 18-5 Checking Available Memory ............................. Deleting Items from Memory ............................ Clearing Entries and List Elements ...................... Resetting the TI-83 ...................................... Memory Management 18-1 Checking Available Memory MEMORY Menu To display the MEMORY menu, press y [MEM]. MEMORY 1: Check RAM... 2: Delete... 3: Clear Entries 4: ClrAllLists 5: Reset... Reports memory availability/usage. Displays DELETE FROM menu. Clears ENTRY (last-entry storage). Clears all lists in memory. Displays RESET menu (all/defaults). Displaying the Check RAM Screen Check RAM displays the Check RAM screen. The top line reports the total amount of available memory. The remaining lines report the amount of memory each variable type is using. You can check this screen to see whether you need to delete variables from memory to make room for new data, such as programs. To check RAM usage, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 1:Check RAM to display the Check RAM screen. The TI-83 expresses memory quantities in bytes. Note: The $ in the left column of the bottom row indicates that you can scroll or page down to view more variable types. Note: Real, List, Y.Vars, and Prgm variable types never reset to zero, even after memory is cleared. To leave the Check RAM screen, press either y [QUIT] or `. Both options display the home screen. 18-2 Memory Management Deleting Items from Memory Deleting an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, picture, graph database, or string), follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 2:Delete to display the DELETE FROM secondary menu. 3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. For example, if you select 4:List, the DELETE:List screen is displayed. 4. Press } and to move the selection cursor (4) next to the item you want to delete, and then press . The variable is deleted from memory. You can delete individual variables one by one from this screen. To leave any DELETE: screen without deleting anything, press y [QUIT], which displays the home screen. Note: You cannot delete some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ. Memory Management 18-3 Clearing Entries and List Elements Clear Entries Clear Entries clears the contents of the ENTRY (last entry) storage area (Chapter 1). To clear the ENTRY storage area, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 3:Clear Entries to paste the instruction to the home screen. 3. Press to clear the ENTRY storage area. To cancel Clear Entries, press `. Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is pasted to the program editor, and the Entry (last entry) is cleared when the program is executed. ClrAllLists ClrAllLists sets to 0 the dimension of each list in memory. To clear all elements from all lists, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 4:ClrAllLists to paste the instruction to the home screen. 3. Press to set to 0 the dimension of each list in memory. To cancel ClrAllLists, press `. ClrAllLists does not delete list names from memory, from the LIST NAMES menu, or from the stat list editor. Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction is pasted to the program editor. The lists are cleared when the program is executed. 18-4 Memory Management Resetting the TI-83 RESET Secondary Menu The RESET secondary menu gives you the option of resetting all memory (including default settings) or resetting the default settings while preserving other data stored in memory, such as programs and Y= functions. Resetting all memory on the TI-83 restores memory to the factory settings. It deletes all nonsystem variables and all programs. It resets all system variables to the default settings. Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data (page 18.3). Resetting All Memory To reset all memory on the TI-83, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 5:Reset to display the RESET secondary menu. 3. Select 1:All Memory to display the RESET MEMORY tertiary menu. 4. Read the message below the RESET MEMORY menu. To cancel memory reset and return to the home screen, select 1:No. To erase from memory all data and programs, select 2:Reset. All factory defaults are restored. Mem cleared is displayed on the home screen. Note: When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast (Chapter 1). Memory Management 18-5 Resetting Defaults When you reset defaults on the TI-83, all defaults are restored to the factory settings. Stored data and programs are not changed. These are some examples of TI-83 defaults that are restored by resetting the defaults. Mode settings such as Normal (notation); Func (graphing); Real (numbers); and Full (screen) Y= functions off Window variable values such as Xmin=L10; Xmax=10; Xscl=1; Yscl=1; and Xres=1 Stat plots off Format settings such as CoordOn (graphing coordinates on); AxesOn; and ExprOn (expression on) rand seed value to 0 To reset all TI-83 factory defaults, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 5:Reset to display the RESET secondary menu. 3. Select 2:Defaults to display the RESET DEFAULTS tertiary menu. 4. Consider the consequences of resetting defaults. To cancel reset and return to the home screen, select 1:No. To restore factory default settings, select 2:Reset. Default settings are restored. Defaults set is displayed on the home screen. 18-6 Memory Management 19 Contents Communication Link Getting Started: Sending Variables ....................... 19-2 TI-83 LINK ............................................... 19-3 Selecting Items to Send .................................. 19-4 Receiving Items .......................................... 19-5 Transmitting Items....................................... 19-6 Transmitting Lists to a TI-82 ............................. 19-8 Transmitting from a TI-82 to a TI-83 ..................... 19-9 Backing Up Memory ..................................... 19-10 Communication Link 19-1 Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-83. 1. On the home screen of the sending unit, press 5 5 Q. Press to store 5.5 to Q. 2. Press y [ [ ] y [ [ ] 1 2 y [ ] ] y [ [ ] 3 4 y [ ] ] y [ ] ] 1. Press to store the matrix to [A]. 3. Connect the calculators with the link cable. Push both ends in firmly. 4. On the receiving unit, press y [LINK] ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. 5. On the sending unit, press y [LINK] to display the SEND menu. 6. Press 2 to select 2:AllN. The AllN SELECT screen is displayed. 7. Press until the selection cursor ( 4 ) is next to [A] MATRX. Press . 8. Press until the selection cursor is next to Q REAL. Press . A square dot next to [A] and Q indicates that each is selected to send. 9. On the sending unit, press ~ to display the TRANSMIT menu. 10. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable. 19-2 Communication Link TI-83 LINK TI-83 Link Capabilities The TI-83 has a port to connect and communicate with another TI-83, a TI-82, the Calculator-Based Laboratory (CBL 2, CBL) System, the Calculator-Based Ranger (CBR), or a personal computer. The unit-to-unit link cable is included with the TI-83. This chapter describes how to communicate with another calculator. You can transfer all variables and programs to another TI-83 or backup the entire memory of a TI-83. The software that enables this communication is built into the TI-83. To transmit from one TI-83 to another, follow the steps on pages 19.6 and 19.7. You can transfer from a TI-82 to a TI-83 all variables and programs. Also, you can transfer from a TI-83 to a TI-82 lists L1 through L6. The software that enables this communication is built into the TI-83. To transmit data from a TI-82 to a TI-83, follow the steps on pages 19.6 and 19.7. You cannot perform a memory backup from a TI-82 to a TI-83. The only data type you can transmit from a TI-83 to a TI-82 is list data stored in L1 through L6. Use the LINK SEND menu item 5:Lists to TI82 (page 19.8). Linking Two TI-83s Linking a TI-82 and a TI-83 Connecting Two Calculators with the Cable 1. Insert either end of the cable into the port very firmly. 2. Insert the other end of the cable into the other calculator's port. CBR and the CBL 2/CBL System are optional accessories that connect to a TI-83 with the unit-to-unit link cable. With a CBR or a CBL 2/CBL and a TI-83, you can collect and analyze real-world data. TI.GRAPH LINK is an optional accessory that links a TI-83 Linking to a CBR or the CBL 2/CBL System Linking to a PC or Macintosh to enable communication with a personal computer. Communication Link 19-3 Selecting Items to Send LINK SEND Menu To display the LINK SEND menu, press y [LINK]. SEND RECEIVE 1: All+... 2: AllN... 3: Prgm... 4: List... 5: Lists to TI82... 6: GDB... 7: Pic... 8: Matrix... 9: Real... 0: Complex... A: Y-Vars... B: String... C: Back Up... Displays all items selected. Displays all items deselected. Displays all programs names. Displays all list names. Displays list names L1 through L6. Displays all graph databases. Displays all picture data types. Displays all matrix data types. Displays all real variables. Displays all complex variables. Displays all Y= variables. Displays all string variables. Selects all for backup to TI-83. When you select an item on the LINK SEND menu, the corresponding SELECT screen is displayed. Note: Each SELECT screen, except All+ SELECT, is displayed initially with no data selected. Selecting Items to Send To select items to send on the sending unit, follow these steps. 1. Press y [LINK] to display the LINK SEND menu. 2. Select the menu item that describes the data type to send. The corresponding SELECT screen is displayed. 3. Press } and to move the selection cursor ( 4 ) to an item you want to select or deselect. 4. Press to select or deselect the item. Selected names are marked with a 0. 5. Repeat steps 3 and 4 to select or deselect additional items. 19-4 Communication Link Receiving Items LINK RECEIVE Menu To display the LINK RECEIVE menu, press y [LINK] ~. SEND RECEIVE 1: Receive Sets unit to receive data transmission. Receiving Unit When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press , and then select 1:Quit from the Error in Xmit menu. To transmit, follow the steps on page 19.6. When transmission is complete, the unit exits the receive mode. You can select 1:Receive again to receive more items. The receiving unit then displays a list of items received. Press y [QUIT] to exit the receive mode. DuplicateName Menu During transmission, if a variable name is duplicated, the DuplicateName menu is displayed on the receiving unit. DuplicateName 1: Rename 2: Overwrite 3: Omit 4: Quit Prompts to rename receiving variable. Overwrites data in receiving variable. Skips transmission of sending variable. Stops transmission at duplicate variable. When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press . Transmission resumes. When you select 2:Overwrite, the sending unit's data overwrites the existing data stored on the receiving unit. Transmission resumes. When you select 3:Omit, the sending unit does not send the data in the duplicated variable name. Transmission resumes with the next item. When you select 4:Quit, transmission stops, and the receiving unit exits receive mode. Insufficient Memory in Receiving Unit During transmission, if the receiving unit does not have sufficient memory to receive an item, the Memory Full menu is displayed on the receiving unit. To skip this item for the current transmission, select 1:Omit. Transmission resumes with the next item. To cancel the transmission and exit receive mode, select 2:Quit. Communication Link 19-5 Transmitting Items Transmitting Items To transmit selected items after you have selected items to send on the sending unit (page 19.4) and set the receiving unit to receive (page 19.5), follow these steps. 1. Press ~ on the sending unit to display the TRANSMIT menu. 2. Confirm that Waiting... is displayed on the receiving unit, which indicates it is set to receive (page 19.5). 3. Press to select 1:Transmit. The name and type of each item are displayed line by line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted. After all selected items have been transmitted, the message Done is displayed on both calculators. Press } and to scroll through the names. Stopping a Transmission To stop a link transmission, press . The Error in Xmit menu is displayed on both units. To leave the error menu, select 1:Quit. A transmission error occurs after one or two seconds if: A cable is not attached to the sending unit. A cable is not attached to the receiving unit. Note: If the cable is attached, push it in firmly and try again. Error Conditions The receiving unit is not set to receive transmission. You attempt a backup between a TI-82 and a TI-83. You attempt a data transfer from a TI-83 to a TI-82 with data other than lists L1 through L6 or without using menu item 5:Lists to TI82. Although a transmission error does not occur, these two conditions may prevent successful transmission. You try to use Get( with a calculator instead of a CBL 2/CBL or CBR. You try to use GetCalc( with a TI-82 instead of a TI-83. 19-6 Communication Link Transmitting Items to an Additional TI-83 After sending or receiving data, you can repeat the same transmission to additional TI-83 units--from either the sending unit or the receiving unit--without having to reselect data to send. The current items remain selected. Note: You cannot repeat transmission if you selected All+ or All.. To transmit to an additional TI-83, follow these steps. 1. Set the TI-83 to receive (page 19.5). 2. Do not select or deselect any new items to send. If you select or deselect an item, all selections or deselections from the previous transmission are cleared. 3. Disconnect the link cable from one TI-83 and connect it to the additional TI-83. 4. Set the additional TI-83 to receive (page 19.5). 5. Press y [LINK] on the sending TI-83 to display the LINK SEND menu. 6. Select the menu item that you used for the last transmission. The data from your last transmission is still selected. 7. Press ~ to display the LINK TRANSMIT menu. 8. Confirm that the receiving unit is set to receive (page 19.5). 9. Press to select 1:Transmit and begin transmitting. Communication Link 19-7 Transmitting Lists to a TI-82 Transmitting Lists to a TI-82 The only data type you can transmit from a TI-83 to a TI-82 is list data stored in L1 through L6. To transmit to a TI-82 the list data that is stored to TI-83 lists L1, L2, L3, L4, L5, or L6, follow these steps. 1. Set the TI-82 to receive (page 19.5). 2. Press y [LINK] 5 on the sending TI-83 to select 5:Lists to TI82. The SELECT screen is displayed. 3. Select each list to transmit. 4. Press ~ to display the LINK TRANSMIT menu. 5. Confirm that the receiving unit is set to receive (page 19.5). 6. Press to select 1:Transmit and begin transmitting. Note: If dimension > 99 for a TI-83 list that is selected to send, the receiving TI-82 will truncate the list at the ninety-ninth element during transmission. 19-8 Communication Link Transmitting from a TI-82 to a TI-83 Resolved Differences between the TI-82 and TI-83 Generally, you can transmit items to a TI-83 from a TI-82, but differences between the two products may affect some transmitted data. This table shows differences for which the software built into the TI-83 automatically adjusts when a TI-83 receives TI-82 data. TI.82 nMin nStart Un Vn UnStart VnStart TblMin TI.83 PlotStart nMin u v u(nMin) v(nMin) TblStart For example, if you transmit from a TI-82 to a TI-83 a program that contains nStart on a command line and then display the program on the receiving TI-83, you will see that nMin has automatically replaced nStart on the command line. Unresolved Differences between the TI-82 and TI-83 The software built into the TI-83 cannot resolve some differences between the TI-82 and TI-83, which are described below. You must edit the data on the TI-83 after you transmit to account for these differences, or the TI-83 will misinterpret the data. The TI-83 reinterprets TI-82 prefix functions to include open parentheses, which may add extraneous parentheses to transmitted expressions. For example, if you transmit sin X+5 from a TI-82 to a TI.83, the TI-83 reinterprets it as sin(X+5. Without a closing parenthesis after X, the TI-83 interprets this as sin(X+5), not the sum of 5 and sin(X). If a TI-82 instruction that the TI-83 cannot translate is transmitted, the ERR:INVALID menu is displayed when the TI-83 attempts to execute the instruction. For example, on the TI-82, the character group Un-1 is pasted to the cursor location when you press y [UnN1]. The TI-83 cannot directly translate Un-1 to the TI-83 syntax u(nN1), so the ERR:INVALID menu is displayed. Note: TI-83 implied multiplication rules differ from those of the TI.82. For example, the TI-83 evaluates 12X as (12)X, while the TI-82 evaluates 12X as 1(2X) (Chapter 2). Communication Link 19-9 Backing Up Memory Memory Backup To copy the exact contents of memory in the sending TI-83 to the memory of the receiving TI-83, put the other unit in receive mode. Then, on the receiving unit, select C:Back Up from the LINK SEND menu. Warning: C:Back Up overwrites the memory in the receiving unit; all information in the memory of the receiving unit is lost. Note: If you do not want to do a backup, select 2:Quit to return to the LINK SEND menu. Select 1:Transmit to begin transmission. Receiving Unit As a safety check to prevent accidental loss of memory, the message WARNING . Backup is displayed when the receiving unit receives notice of a backup. To continue with the backup process, select 1:Continue. The backup transmission begins. To prevent the backup, select 2:Quit. Note: If a transmission error is returned during a backup, the receiving unit is reset. Memory Backup Complete When the backup is complete, both the sending calculator and receiving calculator display a confirmation screen. 19-10 Communication Link A Contents Tables and Reference Information Table of Functions and Instructions ..................... TI.83 Menu Map ......................................... Variables ................................................ Statistics Formulas ...................................... Financial Formulas ...................................... A-2 A-39 A-49 A-50 A-54 Tables and Reference Information A-1 Table of Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table. From the CATALOG, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as they appear in the CATALOG. indicates keystrokes that are valid in the program editor only. Some keystrokes display menus that are available only in the program editor. Others paste mode, format, or table-set instructions only when you are in the program editor. Function or Instruction/ Arguments abs(value) Key or Keys/ Menu or Screen/Item Result Returns the absolute value of a real number, expression, list, or matrix. Returns the magnitude of a complex number or list. Returns 1 if both valueA and valueB are 0. valueA and valueB can be real numbers, expressions, or lists. Returns the polar angle of a complex number or list of complex numbers. Performs a one-way analysis of variance for comparing the means of two to 20 populations. Returns the last answer. NUM 1:abs( 2-13 10-10 2-19 abs(complex value) CPX 5:abs( valueA and valueB y [TEST] LOGIC 1:and 2-26 CPX 4:angle( angle(value) 2-19 ANOVA(list1,list2 [,list3,...,list20]) ... TESTS F:ANOVA( Ans y [ANS] 13-25 1-18 A-2 Tables and Reference Information Function or Instruction/ Arguments Result augment(matrixA,matrixB) Returns a matrix, which is matrixB appended to matrixA as new columns. Returns a list, which is listB augment(listA,listB) concatenated to the end of listA. Turns off the graph axes. AxesOff AxesOn a+bi Key or Keys/ Menu or Screen/Item MATH 7:augment( 10-14 11-15 3-14 3-14 1-12 y [LIST] OPS 9:augment( y [FORMAT] AxesOff Turns on the graph axes. y [FORMAT] AxesOn Sets the mode to rectangular complex number mode (a+bi). Computes the balance at npmt bal(npmt[,roundvalue]) for an amortization schedule using stored values for PV, , and PMT and rounds the computation to roundvalue. binomcdf(numtrials,p[,x]) Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial. binompdf(numtrials,p[,x]) Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial. c2cdf(lowerbound, Computes the c2 distribution upperbound,df) probability between lowerbound and upperbound for the specified degrees of freedom df. z a+bi y [FINANCE] CALC 9:bal( 14-9 y [DISTR] DISTR A:binomcdf( 13-33 y [DISTR] DISTR 0:binompdf( 13-33 y [DISTR] DISTR 7:c2cdf( 13-31 Tables and Reference Information A-3 Function or Instruction/ Arguments c2pdf(x,df) c2.Test(observedmatrix, expectedmatrix [,drawflag]) Circle(X,Y,radius) Result Computes the probability density function (pdf) for the c2 distribution at a specified x value for the specified degrees of freedom df. Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results. Draws a circle with center (X,Y) and radius. Key or Keys/ Menu or Screen/Item y [DISTR] DISTR 6:c2pdf( 13-31 ... TESTS C:c2.Test( 13-22 8-11 y [DRAW] DRAW 9:Circle( Clear Entries Clears the contents of the Last y [MEM] MEMORY Entry storage area. 3:Clear Entries 18-4 ClrAllLists Sets to 0 the dimension of all lists in memory. y [MEM] MEMORY 4:ClrAllLists 18-4 8-4 16-20 12-20 16-20 2-18 1-11 ClrDraw Clears all drawn elements from y [DRAW] DRAW a graph or drawing. 1:ClrDraw ClrHome Clears the home screen. I/O 8:ClrHome ClrList listname1 [,listname2, ..., Sets to 0 the dimension of one or more listnames. Clears all values from the table. Returns the complex conjugate of a complex number or list of complex numbers. Sets connected plotting mode; resets all Y= editor graph-style settings to . ... EDIT 4:ClrList listname n] ClrTable I/O 9:ClrTable conj(value) CPX 1:conj( Connected z Connected A-4 Tables and Reference Information Function or Instruction/ Arguments CoordOff CoordOn cos(value) cosL1(value) cosh(value) coshL1(value) CubicReg [Xlistname, Ylistname,freqlist, regequ] cumSum(list) cumSum(matrix) dbd(date1,date2) value4Dec Result Turns off cursor coordinate value display. Turns on cursor coordinate value display. Returns cosine of a real number, expression, or list. Returns arccosine of a real number, expression, or list. Returns hyperbolic cosine of a real number, expression, or list. Returns hyperbolic arccosine of a real number, expression, or list. Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Returns a list of the cumulative sums of the elements in list, starting with the first element. Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom. Calculates the number of days between date1 and date2 using the actual-day-count method. Displays a real or complex number, expression, list, or matrix in decimal format. Key or Keys/ Menu or Screen/Item y [FORMAT] CoordOff 3-14 3-14 2-3 y [FORMAT] CoordOn TM y [COSL1] 2-3 y [CATALOG] cosh( 15-10 y [CATALOG] coshL1( 15-10 ... CALC 6:CubicReg 12-26 y [LIST] OPS 6:cumSum( 11-12 MATH 0:cumSum( 10-15 y [FINANCE] CALC D:dbd( 14-13 2-5 MATH 2:4Dec Tables and Reference Information A-5 Function or Instruction/ Arguments Degree DelVar variable Result Sets degree angle mode. Deletes from memory the contents of variable. Sets table to ask for dependent-variable values. Sets table to generate dependent-variable values automatically. Returns determinant of matrix. Sets diagnostics-off mode; r, r2, and R2 are not displayed as regression model results. Sets diagnostics-on mode; r, r2, and R2 are displayed as regression model results. Returns the dimension of listname. Returns the dimension of matrixname as a list. Assigns a new dimension (length) to a new or existing listname. Assigns new dimensions to a new or existing matrixname. Displays the home screen. Key or Keys/ Menu or Screen/Item z Degree 1-11 16-15 7-3 7-3 CTL G:DelVar DependAsk DependAuto y [TBLSET] Depend: Ask y [TBLSET] Depend: Auto det(matrix) MATH 1:det( 10-12 12-23 DiagnosticOff y [CATALOG] DiagnosticOff DiagnosticOn y [CATALOG] DiagnosticOn 12-23 y [LIST] OPS 3:dim( dim(listname) 11-11 10-12 11-11 10-13 16-18 16-18 dim(matrixname) MATH 3:dim( length!dim(listname) y [LIST] OPS 3:dim( {rows,columns}! dim(matrixname) Disp MATH 3:dim( I/O 3:Disp Disp [valueA,valueB, valueC,...,value n] Displays each value. I/O 3:Disp A-6 Tables and Reference Information Function or Instruction/ Arguments DispGraph Result Displays the graph. Key or Keys/ Menu or Screen/Item I/O 4:DispGraph 16-19 DispTable Displays the table. I/O 5:DispTable 16-19 value4DMS Displays value in DMS format. y [ANGLE] ANGLE 4:4DMS 2-24 1-11 8-9 Dot DrawF expression Sets dot plotting mode; resets z all Y= editor graph-style settings Dot to . Draws expression (in terms of y [DRAW] X) on the graph. DRAW 6:DrawF DrawInv expression :DS<(variable,value) :commandA :commands e^(power) e^(list) Draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis. Decrements variable by 1; skips commandA if variable < value. Returns e raised to power. Returns a list of e raised to a list of powers. Returns value times 10 to the exponent. Returns list elements times 10 to the exponent. Returns matrix elements times 10 to the exponent. Computes the effective interest rate. y [DRAW] DRAW 8:DrawInv 8-9 CTL B:DS<( 16-14 2-4 y [ex] y [ex] 2-4 y [EE] 1-7 y [EE] 1-7 y [EE] 1-7 y [FINANCE] CALC C:4Eff( Exponent: valueEexponent Exponent: listEexponent Exponent: matrixEexponent 4Eff(nominal rate, compounding periods) Else 14-12 See If:Then:Else Tables and Reference Information A-7 Function or Instruction/ Arguments End Eng Equ4String(Y= var,Strn) Key or Keys/ Result Menu or Screen/Item Identifies end of For(, CTL If-Then-Else, Repeat, or While loop. 7:End 16-12 Sets engineering display mode. z Eng 1-10 15-7 expr(string) ExpReg [Xlistname, Ylistname,freqlist,regequ] ExprOff ExprOn cdf(lowerbound, upperbound, numerator df, denominator df) Fill(value,matrixname) Converts the contents of a Y= var to a string and stores it in Strn. Converts string to an expression and executes it. Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Turns off the expression display during TRACE. Turns on the expression display during TRACE. Computes the distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. Stores value to each element in matrixname. y [CATALOG] Equ4String( y [CATALOG] expr( 15-7 ... CALC 0:ExpReg 12-26 y [FORMAT] ExprOff 3-14 3-14 y [FORMAT] ExprOn y [DISTR] DISTR 9:cdf( 13-32 MATH 4:Fill( 10-13 11-11 1-10 1-10 Fill(value,listname) Stores value to each element in y [LIST] listname. OPS 4:Fill( Fix # Sets fixed-decimal mode for # of decimal places. Sets floating decimal mode. z 0123456789 Float (select one) z Float A-8 Tables and Reference Information Function or Instruction/ Arguments fMax(expression,variable, lower,upper[,tolerance]) fMin(expression,variable, lower,upper[,tolerance]) fnInt(expression,variable, lower,upper[,tolerance]) FnOff [function#, function#,...,function n] FnOn [function#, function#,...,function n] :For(variable,begin,end [,increment]) :commands :End :commands fPart(value) Result Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified tolerance. Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance. Returns the function integral of expression with respect to variable, between lower and upper, with specified tolerance. Deselects all Y= functions or specified Y= functions. Selects all Y= functions or specified Y= functions. Key or Keys/ Menu or Screen/Item MATH 7:fMax( 2-6 MATH 6:fMin( 2-6 MATH 9:fnInt( 2-7 Y-VARS On/Off 2:FnOff 3-8 3-8 Y-VARS On/Off 1:FnOn Executes commands through End, incrementing variable CTL from begin by increment until 4:For( variable>end. 16-10 Returns the fractional part or parts of a real or complex number, expression, list, or matrix. Computes the distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. NUM 4:fPart( 2-14 10-11 pdf(x,numerator df, denominator df) y [DISTR] DISTR 8:pdf( 13-32 Tables and Reference Information A-9 Function or Instruction/ Arguments value4Frac Full Func gcd(valueA,valueB) Result Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms. Sets full screen mode. Sets function graphing mode. Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists. Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. Gets data from the CBL 2/CBL System or CBR and stores it in variable. Gets contents of variable on another TI.83 and stores it to variable on the receiving TI.83. Returns the key code for the current keystroke, or 0, if no key is pressed. Transfers control to label. Key or Keys/ Menu or Screen/Item MATH 1:4Frac 2-5 z Full 1-12 1-11 z Func NUM 9:gcd( 2-15 y [DISTR] DISTR E:geometcdf( geometcdf(p,x) 13-34 y [DISTR] DISTR D:geometpdf( geometpdf(p,x) 13-34 I/O A:Get( Get(variable) 16-21 16-21 16-20 16-13 GetCalc(variable) I/O 0:GetCalc( getKey I/O 7:getKey Goto label CTL 0:Goto A-10 Tables and Reference Information Function or Instruction/ Arguments GraphStyle(function#, graphstyle#) Result Sets a graphstyle for function#. Key or Keys/ Menu or Screen/Item CTL H:GraphStyle( 16-15 GridOff GridOn G-T Horiz Horizontal y Turns off grid format. Turns on grid format. Sets graph-table vertical split-screen mode. Sets horizontal split-screen mode. Draws a horizontal line at y. y [FORMAT] GridOff 3-14 3-14 1-12 1-12 8-6 10-13 16-9 y [FORMAT] GridOn z G-T z Horiz y [DRAW] DRAW 3:Horizontal identity(dimension) :If condition :commandA :commands :If condition :Then :commands :End :commands :If condition :Then :commands :Else :commands :End :commands imag(value) Returns the identity matrix of dimension rows dimension columns. If condition = 0 (false), skips commandA. Executes commands from Then to End if condition = 1 (true). MATH 5:identity( CTL 1:If CTL 2:Then 16-9 Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = 0 (false). CTL 3:Else 16-10 Returns the imaginary (nonreal) part of a complex number or list of complex numbers. CPX 3:imag( 2-18 Tables and Reference Information A-11 Function or Instruction/ Arguments IndpntAsk IndpntAuto Input Result Sets table to ask for independent-variable values. Sets table to generate independent-variable values automatically. Displays graph. Key or Keys/ Menu or Screen/Item y [TBLSET] Indpnt: Ask 7-3 7-3 y [TBLSET] Indpnt: Auto I/O 1:Input 16-16 16-17 16-17 15-7 Input [variable] Input ["text",variable] Input [Strn,variable] Prompts for value to store to variable. Displays Strn and stores entered value to variable. Returns the character position in string of the first character of substring beginning at start. Returns the largest integer a real or complex number, expression, list, or matrix. Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule. Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by m and s. Returns the integer part of a real or complex number, expression, list, or matrix. I/O 1:Input I/O 1:Input inString(string,substring [,start]) int(value) y [CATALOG] inString( NUM 5:int( 2-14 10-11 GInt(pmt1,pmt2 [,roundvalue]) y [FINANCE] CALC A:GInt( 14-9 y [DISTR] DISTR 3:invNorm( invNorm(area[,m,s]) 13-30 NUM 3:iPart( iPart(value) 2-14 10-11 A-12 Tables and Reference Information Function or Instruction/ Arguments irr(CF0,CFList[,CFFreq]) Result Returns the interest rate at which the net present value of the cash flows is equal to zero. Increments variable by 1; skips commandA if variable>value. Identifies the next one to five characters as a user-created list name. Turns off axes labels. Turns on axes labels. Creates a label of one or two characters. Returns the least common multiple of valueA and valueB, which can be real numbers or lists. Returns the number of characters in string. Draws a line from (X1,Y1) to (X2,Y2). Erases a line from (X1,Y1) to (X2,Y2). Key or Keys/ Menu or Screen/Item y [FINANCE] CALC 8:irr( 14-8 :IS>(variable,value) :commandA :commands listname CTL A:IS>( 16-13 y [LIST] OPS B: 11-16 3-14 3-14 16-13 LabelOff LabelOn Lbl label y [FORMAT] LabelOff y [FORMAT] LabelOn CTL 9:Lbl lcm(valueA,valueB) NUM 8:lcm( 2-15 y [CATALOG] length( length(string) Line(X1,Y1,X2,Y2) 15-8 8-5 8-5 y [DRAW] DRAW 2:Line( Line(X1,Y1,X2,Y2,0) y [DRAW] DRAW 2:Line( Tables and Reference Information A-13 Function or Instruction/ Arguments LinReg(a+bx) [Xlistname, Ylistname,freqlist, regequ] Result Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. LinReg(ax+b) [Xlistname, Fits a linear regression model Ylistname,freqlist, to Xlistname and Ylistname regequ] with frequency freqlist, and stores the regression equation to regequ. Performs a linear regression LinRegTTest [Xlistname, Ylistname,freqlist, and a t-test. alternative=L1 is alternative,regequ] <; alternative=0 is ; alternative=1 is >. @List(list) Returns a list containing the differences between consecutive elements in list. Fills matrixname column by List 4 matr(listname1,..., listname n,matrixname) column with the elements from each specified listname. ln(value) Key or Keys/ Menu or Screen/Item ... CALC 8:LinReg(a+bx) 12-26 ... CALC 4:LinReg(ax+b) 12-25 ... TESTS E:LinRegTTest 13-24 y [LIST] OPS 7:@List( 11-12 10-14 11-15 2-4 y [LIST] OPS 0:List 4 matr( LnReg [Xlistname, Ylistname,freqlist, regequ] log(value) Returns the natural logarithm of a real or complex number, expression, or list. Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Returns logarithm of a real or complex number, expression, or list. ... CALC 9:LnReg 12-26 2-4 A-14 Tables and Reference Information Function or Instruction/ Arguments Logistic [Xlistname, Ylistname,freqlist, regequ] Result Fits a logistic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Fills each listname with Matr 4 list(matrix, listnameA,...,listname n) elements from each column in matrix. Fills a listname with elements Matr 4 list(matrix, column#,listname) from a specified column# in matrix. Returns the larger of valueA max(valueA,valueB) and valueB. max(list) Key or Keys/ Menu or Screen/Item ... CALC B:Logistic 12-27 y [LIST] OPS A:Matr 4 list( 10-14 11-16 10-14 11-16 2-15 11-16 y [LIST] OPS A:Matr 4 list( NUM 7:max( Returns largest real or complex element in list. y [LIST] MATH 2:max( max(listA,listB) Returns a real or complex list of y [LIST] the larger of each pair of MATH elements in listA and listB. 2:max( 11-16 max(value,list) mean(list[,freqlist]) Returns a real or complex list of the larger of value or each list element. Returns the mean of list with frequency freqlist. y [LIST MATH 2:max( 11-16 11-16 11-16 y [LIST] MATH 3:mean( median(list[,freqlist]) Returns the median of list with y [LIST] frequency freqlist. MATH 4:median( Med-Med [Xlistname, Ylistname,freqlist, regequ] Menu("title","text1",label1 [,...,"text7",label7]) Fits a median-median model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Generates a menu of up to seven items during program execution. ... CALC 3:Med-Med 12-25 CTL C:Menu( 16-14 Tables and Reference Information A-15 Function or Instruction/ Arguments min(valueA,valueB) Result Returns smaller of valueA and valueB. Returns smallest real or complex element in list. Key or Keys/ Menu or Screen/Item NUM 6:min( 2-15 11-16 11-16 11-16 2-21 2-21 2-21 min(list) y [LIST] MATH 1:min( Returns real or complex list of the smaller of each pair of elements in listA and listB. Returns a real or complex list min(value,list) of the smaller of value or each list element. valueA nCr valueB Returns the number of combinations of valueA taken valueB at a time. value nCr list Returns a list of the combinations of value taken each element in list at a time. list nCr value Returns a list of the combinations of each element in list taken value at a time. listA nCr listB Returns a list of the combinations of each element in listA taken each element in listB at a time. nDeriv(expression,variable, Returns approximate value[,H]) numerical derivative of expression with respect to variable at value, with specified H. 4Nom(effective rate, Computes the nominal interest compounding periods) rate. min(listA,listB) Normal y [LIST] MATH 1:min( y [LIST] MATH 1:min( PRB 3:nCr PRB 3:nCr PRB 3:nCr PRB 3:nCr 2-21 MATH 8:nDeriv( 2-7 y [FINANCE] CALC B:4Nom( 14-12 1-10 Sets normal display mode. z Normal A-16 Tables and Reference Information Function or Instruction/ Arguments normalcdf(lowerbound, upperbound[,m,s]) normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value listA nPr listB npv(interest rate,CF0, CFList[,CFFreq]) valueA or valueB Result Computes the normal distribution probability between lowerbound and upperbound for the specified m and s. Computes the probability density function for the normal distribution at a specified x value for the specified m and s. Returns 0 if value is 0. value can be a real number, expression, or list. Returns the number of permutations of valueA taken valueB at a time. Returns a list of the permutations of value taken each element in list at a time. Returns a list of the permutations of each element in list taken value at a time. Returns a list of the permutations of each element in listA taken each element in listB at a time. Computes the sum of the present values for cash inflows and outflows. Returns 1 if valueA or valueB is 0. valueA and valueB can be real numbers, expressions, or lists. Key or Keys/ Menu or Screen/Item y [DISTR] DISTR 2:normalcdf( 13-27 y [DISTR] DISTR 1:normalpdf( 13-29 y [TEST] LOGIC 4:not( 2-26 2-21 2-21 2-21 PRB 2:nPr PRB 2:nPr PRB 2:nPr PRB 2:nPr 2-21 y [FINANCE] CALC 7:npv( 14-8 y [TEST] LOGIC 2:or 2-26 Tables and Reference Information A-17 Function or Instruction/ Arguments Result Output(row,column,"text") Displays text beginning at specified row and column. Output(row,column,value) Key or Keys/ Menu or Screen/Item I/O 6:Output( 16-19 16-19 1-11 16-12 Displays value beginning at specified row and column. Sets parametric graphing mode. Suspends program execution until you press . Displays value; suspends program execution until you press . Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlistname and Ylistname using mark. Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for Xlistname with frequency freqlist. Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname with frequency freqlist using mark. Defines Plot# (1, 2, or 3) of type NormProbPlot for datalistname on data axis using mark. data axis can be X or Y. Deselects all stat plots or one or more specified stat plots (1, 2, or 3). Selects all stat plots or one or more specified stat plots (1, 2, or 3). I/O 6:Output( Param Pause z Par CTL 8:Pause Pause [value] 16-12 y [STAT PLOT] PLOTS 1:Plot1( 2:Plot2( 3:Plot3( PLOTS 1:Plot1( 2:Plot2( 3:Plot3( PLOTS 1:Plot1( 2:Plot2( 3:Plot3( PLOTS 1:Plot1( 2:Plot2( 3:Plot3( CTL 8:Pause Plot#(type,Xlistname, Ylistname,mark) Plot#(type,Xlistname, freqlist) 12-37 y [STAT PLOT] Plot#(type,Xlistname, freqlist,mark) 12-37 y [STAT PLOT] Plot#(type,datalistname, data axis,mark) 12-37 y [STAT PLOT] PlotsOff [1,2,3] 12-37 y [STAT PLOT] STAT PLOTS 4:PlotsOff STAT PLOTS 5:PlotsOn PlotsOn [1,2,3] 12-35 y [STAT PLOT] 12-35 A-18 Tables and Reference Information Function or Instruction/ Arguments Pmt_Bgn Pmt_End poissoncdf(m,x) poissonpdf(m,x) Polar Result Specifies an annuity due, where payments occur at the beginning of each payment period. Specifies an ordinary annuity, where payments occur at the end of each payment period. Computes a cumulative probability at x for the discrete Poisson distribution with specified mean m. Computes a probability at x for the discrete Poisson distribution with the specified mean m. Sets polar graphing mode. Displays complex value in polar format. Sets polar graphing coordinates format. Executes the program name. Key or Keys/ Menu or Screen/Item y [FINANCE] CALC F:Pmt_Bgn 14-13 y [FINANCE] CALC E:Pmt_End 14-13 y [DISTR] DISTR C:poissoncdf( 13-34 y [DISTR] DISTR B:poissonpdf( 13-33 z Pol 1-11 2-19 3-13 16-15 complex value 4Polar CPX 7:4Polar PolarGC prgmname y [FORMAT] PolarGC CTRL D:prgm GPrn(pmt1,pmt2 [,roundvalue]) Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule. Returns product of list prod(list[,start,end]) elements between start and end. Prompts for value for Prompt variableA [,variableB,...,variable n] variableA, then variableB, and so on. y [FINANCE] CALC 0:GPrn( 14-9 y [LIST] MATH 6:prod( 11-18 16-18 I/O 2:Prompt Tables and Reference Information A-19 Function or Instruction/ Arguments 1.PropZInt(x,n [,confidence level]) 2.PropZInt(x1,n1,x2,n2 [,confidence level]) 1.PropZTest(p0,x,n [,alternative,drawflag]) Result Computes a one-proportion z confidence interval. Computes a two-proportion z confidence interval. Key or Keys/ Menu or Screen/Item ... TESTS A:1.PropZInt( 13-20 ... TESTS B:2.PropZInt( 13-21 2.PropZTest(x1,n1,x2,n2 [,alternative,drawflag]) Pt.Change(x,y) Computes a one-proportion ... z test. alternative=L1 is <; TESTS alternative=0 is ; 5:1.PropZTest( alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. 13-14 Computes a two-proportion ... z test. alternative=L1 is <; TESTS alternative=0 is ; 6:2.PropZTest( alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. 13-15 y [DRAW] Reverses a point at (x,y). POINTS 3:Pt.Change( 8-15 8-15 8-14 Pt.Off(x,y[,mark]) Erases a point at (x,y) using mark. Draws a point at (x,y) using mark. Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. y [DRAW] POINTS 2:Pt.Off( Pt.On(x,y[,mark]) y [DRAW] POINTS 1:Pt.On( PwrReg [Xlistname, Ylistname,freqlist, ... CALC A:PwrReg regequ] 12-27 A-20 Tables and Reference Information Function or Instruction/ Arguments Pxl.Change(row,column) Pxl.Off(row,column) Pxl.On(row,column) pxl.Test(row,column) P4Rx(r,q) P4Ry(r,q) QuadReg [Xlistname, Ylistname,freqlist, regequ] QuartReg [Xlistname, Ylistname,freqlist, regequ] Radian rand[(numtrials)] Result Reverses pixel at (row,column); 0 row 62 and 0 column 94. Erases pixel at (row,column); 0 row 62 and 0 column 94. Draws pixel at (row,column); 0 row 62 and 0 column 94. Returns 1 if pixel (row, column) is on, 0 if it is off; 0 row 62 and 0 column 94. Returns X, given polar coordinates r and q or a list of polar coordinates. Returns Y, given polar coordinates r and q or a list of polar coordinates. Fits a quadratic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Fits a quartic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Sets radian angle mode. Returns a random number between 0 and 1 for a specified number of trials numtrials. Generates and displays a random real number from a specified Binomial distribution. Key or Keys/ Menu or Screen/Item y [DRAW POINTS 6:Pxl.Change( 8-16 8-16 8-16 y [DRAW] POINTS 5:Pxl.Off( y [DRAW] POINTS 4:Pxl.On( y [DRAW] POINTS 7:pxl.Test( 8-16 y [ANGLE] ANGLE 7:P4Rx( 2-24 2-24 y [ANGLE] ANGLE 8:P4Ry( ... CALC 5:QuadReg 12-25 ... CALC 7:QuartReg 12-26 z Radian 1-11 PRB 1:rand 2-20 PRB 7:randBin( randBin(numtrials,prob [,numsimulations]) 2-22 Tables and Reference Information A-21 Function or Instruction/ Arguments randInt( lower,upper [,numtrials]) randM(rows,columns) Result Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials. Returns a random matrix of rows (199) columns (199). Key or Keys/ Menu or Screen/Item PRB 5:randInt( 2-22 MATH 6:randM( 10-13 randNorm(m,s[,numtrials]) Generates and displays a PRB 6:randNorm( re^qi Real real(value) RecallGDB n RecallPic n random real number from a specified Normal distribution specified by m and s for a specified number of trials numtrials. Sets the mode to polar complex number mode (re^qi). Sets mode to display complex results only when you enter complex numbers. Returns the real part of a complex number or list of complex numbers. Restores all settings stored in the graph database variable GDBn. Displays the graph and adds the picture stored in Picn. Displays complex value or list in rectangular format. Sets rectangular graphing coordinates format. Returns the row-echelon form of a matrix. 2-22 z re^qi z Real 1-12 1-12 CPX 2:real( 2-18 8-20 8-18 2-19 3-13 10-15 y [DRAW] STO 4:RecallGDB y [DRAW] STO 2:RecallPic complex value 4Rect CPX 6:4Rect RectGC ref(matrix) y [FORMAT] RectGC MATH A:ref( A-22 Tables and Reference Information Function or Instruction/ Arguments :Repeat condition :commands :End :commands Return Result Executes commands until condition is true. Key or Keys/ Menu or Screen/Item CTL 6:Repeat 16-11 Returns to the calling program. CTL E:Return 16-15 2-13 10-16 10-16 round(value[,#decimals]) row(value,matrix,row) row+(matrix,rowA,rowB) row+(value,matrix, rowA,rowB) rowSwap(matrix,rowA, rowB) rref(matrix) Returns a number, expression, list, or matrix rounded to #decimals ( 9). Returns a matrix with row of matrix multiplied by value and stored in row. Returns a matrix with rowA of matrix added to rowB and stored in rowB. Returns a matrix with rowA of matrix multiplied by value, added to rowB, and stored in rowB. Returns a matrix with rowA of matrix swapped with rowB. Returns the reduced rowechelon form of a matrix. Returns R, given rectangular coordinates x and y or a list of rectangular coordinates. Returns q, given rectangular coordinates x and y or a list of rectangular coordinates. NUM 2:round( MATH E:row( MATH D:row+( MATH F:row+( 10-16 MATH C:rowSwap( 10-16 10-15 2-24 2-24 MATH B:rref( R4Pr(x,y) y [ANGLE] ANGLE 5:R4Pr( R4Pq(x,y) y [ANGLE] ANGLE 6:R4Pq( Tables and Reference Information A-23 Function or Instruction/ Arguments 2.SampTest [listname1, listname2,freqlist1, freqlist2,alternative, drawflag] (Data list input) 2.SampTest Sx1,n1, Sx2,n2[,alternative, drawflag] (Summary stats input) 2.SampTInt [listname1, listname2, freqlist1,freqlist2, confidence level,pooled] Result Performs a two-sample test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Performs a two-sample test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances. Key or Keys/ Menu or Screen/Item ... TESTS D:2.SampTest 13-23 ... TESTS D:2.SampTest 13-23 ... TESTS 0:2.SampTInt (Data list input) 2.SampTInt v1,Sx1,n1, v2,Sx2,n2 [,confidence level,pooled] (Summary stats input) 2.SampTTest [listname1, listname2,freqlist1, freqlist2,alternative, pooled,drawflag] (Data list input) 13-19 Computes a two-sample t ... TESTS confidence interval. pooled=1 pools variances; pooled=0 does 0:2.SampTInt not pool variances. 13-19 Computes a two-sample t test. ... alternative=L1 is <; TESTS alternative=0 is ; 4:2.SampTTest alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results. 13-13 A-24 Tables and Reference Information Function or Instruction/ Arguments 2.SampTTest v1,Sx1,n1, v2,Sx2,n2[,alternative, pooled,drawflag] (Summary stats input) 2.SampZInt(s1,s2 [,listname1,listname2, freqlist1,freqlist2, confidence level]) Key or Keys/ Result Menu or Screen/Item Computes a two-sample t test. ... alternative=L1 is <; TESTS alternative=0 is ; 4:2.SampTTest alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results. 13-13 Computes a two-sample z ... confidence interval. TESTS 9:2.SampZInt( (Data list input) 2.SampZInt(s1,s2, v1,n1,v2,n2 [,confidence level]) (Summary stats input) 2.SampZTest(s1,s2 [,listname1,listname2, freqlist1,freqlist2, alternative,drawflag]) (Data list input) 2.SampZTest(s1,s2, v1,n1,v2,n2 [,alternative,drawflag]) 13-18 Computes a two-sample z confidence interval. ... TESTS 9:2.SampZInt( 13-18 Computes a two-sample z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Computes a two-sample z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Sets scientific notation display mode. Selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, Xlistname and Ylistname. ... TESTS 3:2.SampZTest( 13-12 ... TESTS 3:2.SampZTest( (Summary stats input) 13-12 z Sci Sci Select(Xlistname, Ylistname) 1-10 y [LIST] OPS 8:Select( 11-12 Tables and Reference Information A-25 Function or Instruction/ Arguments Send(variable) Key or Keys/ Result Menu or Screen/Item Sends contents of variable to the CBL 2/CBL System or CBR. I/O B:Send( 16-21 seq(expression,variable, begin,end[,increment]) Seq Sequential SetUpEditor Returns list created by evaluating expression with regard to variable, from begin to end by increment. Sets sequence graphing mode. Sets mode to graph functions sequentially. Removes all list names from the stat list editor, and then restores list names L1 through L6 to columns 1 through 6. Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1. Draws lowerfunc and upperfunc in terms of X on the current graph and uses pattern and patres to shade the area bounded by lowerfunc, upperfunc, Xleft, and Xright. Draws the density function for the c2 distribution specified by degrees of freedom df and shades the area between lowerbound and upperbound. y [LIST] OPS 5:seq( 11-11 z Seq 1-11 1-12 z Sequential ... EDIT 5:SetUpEditor 12-21 ... EDIT 5:SetUpEditor SetUpEditor listname1 [,listname2,..., listname20] 12-21 y [DRAW] DRAW 7:Shade( Shade(lowerfunc, upperfunc[,Xleft,Xright, pattern,patres]) 8-10 y [DISTR] DRAW 3:Shadec2( Shadec2(lowerbound, upperbound,df) 13-36 A-26 Tables and Reference Information Function or Instruction/ Arguments Shade(lowerbound, upperbound, numerator df, denominator df) ShadeNorm(lowerbound, upperbound[,m,s]) Shade_t(lowerbound, upperbound,df) Simul sin(value) sinL1(value) sinh(value) sinhL1(value) Result Draws the density function for the distribution specified by numerator df and denominator df and shades the area between lowerbound and upperbound. Draws the normal density function specified by m and s and shades the area between lowerbound and upperbound. Draws the density function for the Student-t distribution specified by degrees of freedom df, and shades the area between lowerbound and upperbound. Sets mode to graph functions simultaneously. Returns the sine of a real number, expression, or list. Returns the arcsine of a real number, expression, or list. Returns the hyperbolic sine of a real number, expression, or list. Returns the hyperbolic arcsine of a real number, expression, or list. Key or Keys/ Menu or Screen/Item y [DISTR] DRAW 4:Shade( 13-36 y [DISTR] DRAW 1:ShadeNorm( 13-35 y [DISTR] DRAW 2:Shade_t( 13-36 z Simul 1-12 2-3 ~ y [SINL1] 2-3 y [CATALOG] sinh( 15-10 y [CATALOG] sinhL1( 15-10 Tables and Reference Information A-27 Function or Instruction/ Arguments SinReg [iterations, Xlistname,Ylistname, period,regequ] Result Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ. solve(expression,variable, Solves expression for variable, guess,{lower,upper}) given an initial guess and lower and upper bounds within which the solution is sought. Sorts elements of listname in SortA(listname) ascending order. Key or Keys/ Menu or Screen/Item ... CALC C:SinReg 12-27 MATH 0:solve( 2-12 y [LIST] OPS 1:SortA( 11-10 12-20 11-10 12-20 11-10 12-20 11-10 12-20 11-18 16-15 1-14 8-19 Sorts elements of keylistname y [LIST] SortA(keylistname, dependlist1[,dependlist2, in ascending order, then sorts OPS each dependlist as a dependent 1:SortA( ...,dependlist n]) SortD(listname) list. Sorts elements of listname in descending order. y [LIST] OPS 2:SortD( Sorts elements of keylistname in descending order, then sorts dependlist1[,dependlist2,..., each dependlist as a dependent dependlist n]) list. Returns the standard deviation stdDev(list[,freqlist]) of the elements in list with frequency freqlist. Ends program execution; Stop returns to home screen. SortD(keylistname, y [LIST] OPS 2:SortD( y [LIST] MATH 7:stdDev( CTL F:Stop Store: value!variable StoreGDB n Stores value in variable. Stores current graph in database GDBn. y [DRAW] STO 3:StoreGDB A-28 Tables and Reference Information Function or Instruction/ Arguments StorePic n Result Stores current picture in picture Picn. Converts string into an equation and stores it in Y= var. Returns a string that is a subset of another string, from begin to length. Returns the sum of elements of list from start to end. Key or Keys/ Menu or Screen/Item y [DRAW] STO 1:StorePic 8-17 15-8 String4Equ(string,Y= var) y [CATALOG] String4Equ( sub(string,begin,length) y [CATALOG] sub( 15-9 y [LIST] MATH 5:sum( sum(list[,start,end]) 11-18 2-3 Returns the tangent of a real number, expression, or list. Returns the arctangent of a tanL1(value) real number, expression, or list. Tangent(expression,value) Draws a line tangent to expression at X=value. tan(value) tanh(value) tanhL1(value) s y [TANL1] 2-3 y [DRAW DRAW 5:Tangent( 8-8 15-10 tcdf(lowerbound, upperbound,df) Text(row,column,text1, text2,...,text n) Returns hyperbolic tangent of a real number, expression, or list. Returns the hyperbolic arctangent of a real number, expression, or list. Computes the Student-t distribution probability between lowerbound and upperbound for the specified degrees of freedom df. Writes text on graph beginning at pixel (row,column), where 0 row 57 and 0 column 94. y [CATALOG] tanh( y [CATALOG] tanhL1( 15-10 y [DISTR] DISTR 5:tcdf( 13-31 y [DRAW] DRAW 0:Text( 8-12 Then See If:Then Tables and Reference Information A-29 Function or Instruction/ Arguments Time TInterval [listname, freqlist,confidence level] Result Sets sequence graphs to plot with respect to time. Computes a t confidence interval. Computes a t confidence interval. Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df. Displays the graph and enters TRACE mode. Performs a t test with frequency freqlist. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Performs a t test with frequency freqlist. alternative=L1 is < ; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Key or Keys/ Menu or Screen/Item y [FORMAT] Time 6-8 13-17 13-17 ... TESTS 8:TInterval (Data list input) TInterval v,Sx,n [,confidence level] (Summary stats input) tpdf(x,df) ... TESTS 8:TInterval y [DISTR] DISTR 4:tpdf( 13-30 r 3-18 ... TESTS 2:T-Test Trace T-Test m0[,listname, freqlist,alternative, drawflag] (Data list input) 13-11 ... TESTS 2:T-Test T-Test m0, v,Sx,n [,alternative,drawflag] (Summary stats input) 13-11 A-30 Tables and Reference Information Function or Instruction/ Arguments tvm_FV[(,,PV,PMT, P/Y,C/Y)] tvm_[(,PV,PMT,FV, P/Y,C/Y)] tvm_[(,PV,PMT,FV, P/Y,C/Y)] tvm_Pmt[(,,PV,FV, P/Y,C/Y)] tvm_PV[(,,PMT,FV, P/Y,C/Y)] uvAxes Result Computes the future value. Key or Keys/ Menu or Screen/Item y [FINANCE] CALC 6:tvm_FV 14-7 14-7 14-7 14-6 14-7 6-8 Computes the annual interest rate. Computes the number of payment periods. Computes the amount of each payment. Computes the present value. y [FINANCE] CALC 3:tvm_ y [FINANCE] CALC 5:tvm_ y [FINANCE] CALC 2:tvm_Pmt y [FINANCE] CALC 4:tvm_PV uwAxes 1-Var Stats [Xlistname, freqlist] 2-Var Stats [Xlistname, Ylistname,freqlist] variance(list[,freqlist]) Vertical x Sets sequence graphs to plot u(n) on the x-axis and v(n) on the y-axis. Sets sequence graphs to plot u(n) on the x-axis and w(n) on the y-axis. Performs one-variable analysis on the data in Xlistname with frequency freqlist. Performs two-variable analysis on the data in Xlistname and Ylistname with frequency freqlist. Returns the variance of the elements in list with frequency freqlist. Draws a vertical line at x. Sets sequence graphs to plot v(n) on the x-axis and w(n) on the y-axis. Sets sequence graphs to trace as webs. y [FORMAT] uv y [FORMAT] uw 6-8 ... CALC 1:1-Var Stats 12-25 ... CALC 2:2-Var Stats 12-25 y [LIST] MATH 8:variance( 11-18 8-6 6-8 y [DRAW] DRAW 4:Vertical vwAxes y [FORMAT] vw Web y [FORMAT] Web 6-8 Tables and Reference Information A-31 Function or Instruction/ Arguments :While condition :commands :End :command valueA xor valueB Result Executes commands while condition is true. Key or Keys/ Menu or Screen/Item CTL 5:While 16-11 ZBox ZDecimal ZInteger Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists. Displays a graph, lets you draw a box that defines a new viewing window, and updates the window. Adjusts the viewing window so that @X=0.1 and @Y=0.1, and displays the graph screen with the origin centered on the screen. Redefines the viewing window using these dimensions: @X=1 @Y=1 Xscl=10 Yscl=10 y [TEST] LOGIC 3:xor 2-26 q ZOOM 1:ZBox 3-20 q ZOOM 4:ZDecimal 3-21 q ZOOM 8:ZInteger 3-22 ... TESTS 7:ZInterval ZInterval s[,listname, freqlist,confidence level] Computes a z confidence interval. Computes a z confidence interval. (Data list input) ZInterval s,v,n [,confidence level] (Summary stats input) Zoom In 13-16 13-16 3-21 3-21 ... TESTS 7:ZInterval Zoom Out Magnifies the part of the graph q ZOOM that surrounds the cursor location. 2:Zoom In Displays a greater portion of q ZOOM the graph, centered on the cursor location. 3:Zoom Out A-32 Tables and Reference Information Function or Instruction/ Arguments ZoomFit ZoomRcl ZoomStat ZoomSto Result Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions. Graphs the selected functions in a user-defined viewing window. Redefines the viewing window so that all statistical data points are displayed. Immediately stores the current viewing window. Replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. Adjusts the X or Y window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window. Replots the functions immediately, updating the window variables to the default values. Key or Keys/ Menu or Screen/Item q ZOOM 0:ZoomFit 3-22 q MEMORY 3:ZoomRcl 3-23 3-22 3-23 q ZOOM 9:ZoomStat q MEMORY 2:ZoomSto ZPrevious q MEMORY 1:ZPrevious 3-23 q ZOOM 5:ZSquare ZSquare 3-21 q ZOOM 6:ZStandard ZStandard 3-22 Tables and Reference Information A-33 Function or Instruction/ Arguments ZNTest(m0,s[,listname, freqlist,alternative, drawflag]) (Data list input) ZNTest(m0,s,v,n [,alternative,drawflag]) (Summary stats input) ZTrig Result Performs a z test with frequency freqlist. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Performs a z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Replots the functions immediately, updating the window variables to preset values for plotting trig functions. Returns factorial of value. Key or Keys/ Menu or Screen/Item ... TESTS 1:Z.Test( 13-10 ... TESTS 1:Z.Test( 13-10 q ZOOM 7:ZTrig 3-22 PRB 4:! Factorial: value! 2-21 2-21 2-23 2-24 Factorial: list! Returns factorial of list elements. Interprets value as degrees; designates degrees in DMS format. Interprets angle as radians. PRB 4:! Degrees notation: value Radian: angler Transpose: matrixT y [ANGLE] ANGLE 1: y [ANGLE] ANGLE 3:r Returns a matrix in which each MATH element (row, column) is swapped with the 2:T corresponding element (column, row) of matrix. 10-12 A-34 Tables and Reference Information Function or Instruction/ Arguments x throotxvalue x throotxlist listxvalue listAxlistB Cube: value3 Result Returns x throot of value. Key or Keys/ Menu or Screen/Item MATH 5:x 2-6 2-6 2-6 2-6 2-6 10-10 2-6 Returns x throot of list elements. Returns list roots of value. MATH 5:x MATH 5:x Returns listA roots of listB. MATH 5:x Returns the cube of a real or complex number, expression, list, or square matrix. Returns the cube root of a real or complex number, expression, or list. Returns 1 if valueA = valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. Returns 1 if valueA valueB. Returns 0 if valueA = valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. Returns 1 if valueA < valueB. Returns 0 if valueA , valueB. valueA and valueB can be real or complex numbers, expressions, or lists. MATH 3:3 Cube root: 3(value) MATH 4:3( Equal: valueA=valueB y [TEST] TEST 1:= 2-25 10-11 y [TEST] TEST 2: Not equal: valueAvalueB 2-25 10-11 y [TEST] TEST 5:< Less than: valueA<valueB 2-25 Tables and Reference Information A-35 Function or Instruction/ Arguments Greater than: valueA>valueB Less than or equal: valueAvalueB Greater than or equal: valueA,valueB Inverse: valueL1 Inverse: listL1 Inverse: matrixL1 Square: value2 Square: list2 Square: matrix2 Powers: value^power Result Returns 1 if valueA > valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, or lists. Returns 1 if valueA valueB. Returns 0 if valueA > valueB. valueA and valueB can be real or complex numbers, expressions, or lists. Returns 1 if valueA , valueB. Returns 0 if valueA < valueB. valueA and valueB can be real or complex numbers, expressions, or lists. Returns 1 divided by a real or complex number or expression. Returns 1 divided by list elements. Returns matrix inverted. Returns value multiplied by itself. value can be a real or complex number or expression. Returns list elements squared. Returns matrix multiplied by itself. Returns value raised to power. value can be a real or complex number or expression. Returns list elements raised to power. Returns value raised to list elements. Key or Keys/ Menu or Screen/Item y [TEST] TEST 3:> 2-25 y [TEST] TEST 6: 2-25 y [TEST] TEST 4:, 2-25 -- 2-3 -- -- 2-3 10-10 2-3 2-3 10-10 > 2-3 > 2-3 > 2-3 Powers: list^power Powers: value^list A-36 Tables and Reference Information Function or Instruction/ Arguments Powers: matrix^power Negation: Lvalue Power of ten: 10^(value) Power of ten: 10^(list) Square root: (value) Multiplication: valueAvalueB Multiplication: valuelist Multiplication: listvalue Multiplication: listAlistB Multiplication: valuematrix Multiplication: matrixAmatrixB Division: valueAvalueB Division: listvalue Division: valuelist Division: listAlistB Result Returns matrix elements raised to power. Returns the negative of a real or complex number, expression, list, or matrix. Returns 10 raised to the value power. value can be a real or complex number or expression. Returns a list of 10 raised to the list power. Returns square root of a real or complex number, expression, or list. Returns valueA times valueB. Returns value times each list element. Returns each list element times value. Returns listA elements times listB elements. Returns value times matrix elements. Returns matrixA times matrixB. Returns valueA divided by valueB. Returns list elements divided by value. Returns value divided by list elements. Returns listA elements divided by listB elements. Key or Keys/ Menu or Screen/Item > 10-10 2-4 10-9 y [10x] 2-4 y [10x] 2-4 y 2-3 2-3 2-3 2-3 2-3 10-9 10-9 2-3 2-3 2-3 2-3 Tables and Reference Information A-37 Function or Instruction/ Arguments Addition: valueA+valueB Addition: list+value Addition: listA+listB Addition: matrixA+matrixB Concatenation: string1+string2 Subtraction: valueANvalueB Subtraction: valueNlist Subtraction: listNvalue Subtraction: listANlistB Subtraction: matrixANmatrixB Minutes notation: degreesminutes' seconds" Seconds notation: degreesminutes' seconds" Result Returns valueA plus valueB. Returns list in which value is added to each list element. Returns listA elements plus listB elements. Returns matrixA elements plus matrixB elements. Concatenates two or more strings. Subtracts valueB from valueA. Subtracts list elements from value. Subtracts value from list elements. Subtracts listB elements from listA elements. Subtracts matrixB elements from matrixA elements. Interprets minutes angle measurement as minutes. Interprets seconds angle measurement as seconds. Key or Keys/ Menu or Screen/Item 2-3 2-3 2-3 10-9 15-6 2-3 2-3 2-3 2-3 10-9 y [ANGLE] ANGLE 2:' 2-23 2-23 A-38 Tables and Reference Information TI-83 Menu Map The TI.83 Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown. o Ŀ (Func mode) Plot1 Plot2 Plot3 Y1= Y2= Y3= Y4= ... Y9= Y0= (Par mode) Plot1 Plot2 Plot3 X1T= Y1T= X2T= Y2T= ... X6T= Y6T= (Pol mode) Plot1 Plot2 Plot3 r1= r2= r3= r4= r5= r6= (Seq mode) Plot1 Plot2 Plot3 nMin=1 u(n)= u(nMin)= v(n)= v(nMin)= w(n)= w(nMin)= y [STAT PLOT] STAT PLOTS 1:Plot1...Off " L1 L2 > 2:Plot2...Off " L1 L2 > 3:Plot3...Off " L1 L2 > 4:PlotsOff 5:PlotsOn y [STAT PLOT] Ŀ (PRGM editor) PLOTS 1:Plot1( 2:Plot2( 3:Plot3( 4:PlotsOff 5:PlotsOn (PRGM editor) TYPE 1:Scatter 2:xyLine 3:Histogram 4:ModBoxplot 5:Boxplot 6:NormProbPlot (PRGM editor) MARK 1:> 2:+ 3: p Ŀ (Func mode) WINDOW Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 Xres=1 (Par mode) WINDOW Tmin=0 Tmax=p2 Tstep=p24 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 (Pol mode) WINDOW qmin=0 qmax=p2 qstep=p24 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 (Seq mode) WINDOW nMin=1 nMax=10 PlotStart=1 PlotStep=1 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 y [TBLSET] TABLE SETUP TblStart=0 @Tbl=1 Indpnt:Auto Ask Depend:Auto Ask y [TBLSET] (PRGM editor) TABLE SETUP Indpnt:Auto Ask Depend:Auto Ask Tables and Reference Information A-39 q Ŀ ZOOM 1:ZBox 2:Zoom In 3:Zoom Out 4:ZDecimal 5:ZSquare 6:ZStandard 7:ZTrig 8:ZInteger 9:ZoomStat 0:ZoomFit MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors... MEMORY (Set Factors...) ZOOM FACTORS XFact=4 YFact=4 y [FORMAT] Ŀ (Func/Par/Pol modes) RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff (Seq mode) Time Web uv vw uw RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff y [CALC] Ŀ (Func mode) CALCULATE 1:value 2:zero 3:minimum 4:maximum 5:intersect 6:dy/dx 7:f(x)dx (Par mode) CALCULATE 1:value 2:dy/dx 3:dy/dt 4:dx/dt (Pol mode) CALCULATE 1:value 2:dy/dx 3:dr/dq (Seq mode) CALCULATE 1:value z Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+b re^q Full Horiz G-T A-40 Tables and Reference Information y [LINK] Ŀ SEND 1:All+... 2:AllN... 3:Prgm... 4:List... 5:Lists to TI82... 6:GDB... 7:Pic... 8:Matrix... 9:Real... 0:Complex... A:Y-Vars... B:String... C:Back Up... RECEIVE 1:Receive ... Ŀ EDIT 1:Edit... 2:SortA( 3:SortD( 4:ClrList 5:SetUpEditor CALC 1:1-Var Stats 2:2-Var Stats 3:Med-Med 4:LinReg(ax+b) 5:QuadReg 6:CubicReg 7:QuartReg 8:LinReg(a+bx) 9:LnReg 0:ExpReg A:PwrReg B:Logistic C:SinReg TESTS 1:Z-Test... 2:T-Test... 3:2-SampZTest... 4:2-SampTTest... 5:1-PropZTest... 6:2-PropZTest... 7:ZInterval... 8:TInterval... 9:2-SampZInt... 0:2-SampTInt... A:1-PropZInt... B:2-PropZInt... C:c 2-Test... D:2-SampTest... E:LinRegTTest... F:ANOVA( Tables and Reference Information A-41 y [LIST] Ŀ NAMES 1:listname 2:listname 3:listname ... OPS 1:SortA( 2:SortD( 3:dim( 4:Fill( 5:seq( 6:cumSum( 7:@List( 8:Select( 9:augment( 0:List4matr( A:Matr4list( B: MATH 1:min( 2:max( 3:mean( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Ŀ MATH 1:4Frac 2:4Dec 3:3 4:3( 5:x 6:fMin( 7:fMax( 8:nDeriv( 9:fnInt( 0:Solver... NUM 1:abs( 2:round( 3:iPart( 4:fPart( 5:int( 6:min( 7:max( 8:lcm( 9:gcd( CPX 1:conj( 2:real( 3:imag( 4:angle( 5:abs( 6:4Rect 7:4Polar PRB 1:rand 2:nPr 3:nCr 4:! 5:randInt( 6:randNorm( 7:randBin( y [TEST] Ŀ TEST 1:= 2: 3:> 4:, 5:< 6: LOGIC 1:and 2:or 3:xor 4:not( A-42 Tables and Reference Information Ŀ NAMES 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] MATH 1:det( 2: T 3:dim( 4:Fill( 5:identity( 6:randM( 7:augment( 8:Matr4list( 9:List4matr( 0:cumSum( A:ref( B:rref( C:rowSwap( D:row+( E:...row( F:...row+( EDIT 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] y [ANGLE] ANGLE 1: 2:' 3: r 4:4DMS 5:R4Pr( 6:R4Pq( 7:P4Rx( 8:P4Ry( Ŀ EXEC 1:name 2:name ... EDIT 1:name 2:name ... NEW 1:Create New Ŀ (PRGM editor) CTL 1:If 2:Then 3:Else 4:For( 5:While 6:Repeat 7:End 8:Pause 9:Lbl 0:Goto A:IS>( B:DS<( C:Menu( D:prgm E:Return F:Stop G:DelVar H:GraphStyle( (PRGM editor) I/O 1:Input 2:Prompt 3:Disp 4:DispGraph 5:DispTable 6:Output( 7:getKey 8:ClrHome 9:ClrTable 0:GetCalc( A:Get( B:Send( (PRGM editor) EXEC 1:name 2:name ... Tables and Reference Information A-43 y [DRAW] Ŀ DRAW 1:ClrDraw 2:Line( 3:Horizontal 4:Vertical 5:Tangent( 6:DrawF 7:Shade( 8:DrawInv 9:Circle( 0:Text( A:Pen POINTS 1:Pt-On( 2:Pt-Off( 3:Pt-Change( 4:Pxl-On( 5:Pxl-Off( 6:Pxl-Change( 7:pxl-Test( STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecallGDB Ŀ VARS 1:Window... 2:Zoom... 3:GDB... 4:Picture... 5:Statistics... 6:Table... 7:String... VARS Y-VARS 1:Function... 2:Parametric... 3:Polar... 4:On/Off... (Window...) X/Y 1:Xmin 2:Xmax 3:Xscl 4:Ymin 5:Ymax 6:Yscl 7:Xres 8:@X 9:@Y 0:XFact A:YFact (Window...) T/q 1:Tmin 2:Tmax 3:Tstep 4:qmin 5:qmax 6:qstep (Window...) U/V/W 1:u(nMin) 2:v(nMin) 3:w(nMin) 4:nMin 5:nMax 6:PlotStart 7:PlotStep A-44 Tables and Reference Information VARS (Zoom...) ZX/ZY 1:ZXmin 2:ZXmax 3:ZXscl 4:ZYmin 5:ZYmax 6:ZYscl 7:ZXres VARS (Zoom...) ZT/Zq 1:ZTmin 2:ZTmax 3:ZTstep 4:Zqmin 5:Zqmax 6:Zqstep (Zoom...) ZU 1:Zu(nMin) 2:Zv(nMin) 3:Zw(nMin) 4:ZnMin 5:ZnMax 6:ZPlotStart 7:ZPlotStep (GDB...) GRAPH DATABASE 1:GDB1 2:GDB2 ... 9:GDB9 0:GDB0 VARS (Picture...) PICTURE 1:Pic1 2:Pic2 ... 9:Pic9 0:Pic0 (Statistics...) XY 1:n 2:v 3:Sx 4:sx 5:w 6:Sy 7:sy 8:minX 9:maxX 0:minY A:maxY (Statistics...) G 1:Gx 2:Gx 2 3:Gy 4:Gy2 5:Gxy (Statistics...) EQ 1:RegEQ 2:a 3:b 4:c 5:d 6:e 7:r 8:r 2 9:R 2 (Statistics...) TEST 1:p 2:z 3:t 4:c 2 5: 6:df 7: 8:1 9:2 0:s A:1 B:2 C:Sx1 D:Sx2 E:Sxp F:n1 G:n2 H:lower I:upper (Statistics...) PTS 1:x1 2:y1 3:x2 4:y2 5:x3 6:y3 7:Q1 8:Med 9:Q 3 Tables and Reference Information A-45 VARS Ŀ (Table...) TABLE 1:TblStart 2:@Tbl 3:TblInput (String...) STRING 1:Str1 2:Str2 3:Str3 4:Str4 ... 9:Str9 0:Str0 Y-VARS Ŀ (Function...) FUNCTION 1:Y1 2:Y2 3:Y3 4:Y4 ... 9:Y9 0:Y0 (Parametric...) PARAMETRIC 1:X1T 2:Y1T 3:X2T 4:Y2T ... A:X6T B:Y6T (Polar...) POLAR 1:r1 2:r2 3:r3 4:r4 5:r5 6:r6 (On/Off...) ON/OFF 1:FnOn 2:FnOff A-46 Tables and Reference Information y [DISTR] Ŀ DISTR 1:normalpdf( 2:normalcdf( 3:invNorm( 4:tpdf( 5:tcdf( 6:c 2 pdf( 7:c 2 cdf( 8:pdf( 9:cdf( 0:binompdf( A:binomcdf( B:poissonpdf( C:poissoncdf( D:geometpdf( E:geometcdf( DRAW 1:ShadeNorm( 2:Shade_t( 3:Shadec 2 ( 4:Shade( y [FINANCE] Ŀ CALC 1:TVM Solver... 2:tvm_Pmt 3:tvm_ 4:tvm_PV 5:tvm_ 6:tvm_FV 7:npv( 8:irr( 9:bal( 0:GPrn( A:GInt( B:4Nom( C:4Eff( D:dbd( E:Pmt_End F:Pmt_Bgn VARS 1: 2: 3:PV 4:PMT 5:FV 6:P/Y 7:C/Y Tables and Reference Information A-47 y [MEM] MEMORY 1:Check RAM... 2:Delete... 3:Clear Entries 4:ClrAllLists 5:Reset... MEMORY Ŀ (Check RAM...) MEM FREE 27225 Real 15 Complex 0 List 0 Matrix 0 Y-Vars 240 Prgm 14 Pic 0 GDB 0 String 0 (Delete...) DELETE FROM... 1:All... 2:Real... 3:Complex... 4:List... 5:Matrix... 6:Y-Vars... 7:Prgm... 8:Pic... 9:GDB... 0:String... (Reset...) RESET 1:All Memory... 2:Defaults... MEMORY (Reset...) y [CATALOG] CATALOG cosh( cosh L1( ... Equ4String( expr( ... inString( ... length( ... sinh( sinh L1( ... String4Equ( sub( ... tanh( tanh L1( (Defaults...) RESET DEFAULTS 1:No 2:Reset Ŀ (All Memory...) RESET MEMORY 1:No 2:Reset Resetting memory erases all data and programs. A-48 Tables and Reference Information Variables User Variables The TI.83 uses the variables listed below in various ways. Some variables are restricted to specific data types. The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI.83 can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data. The variables (list names) L1 through L6 are restricted to lists; you cannot store another type of data to them. The variables (matrix names) [A] through [J] are restricted to matrices; you cannot store another type of data to them. The variables Pic1 through Pic9 and Pic0 are restricted to pictures; you cannot store another type of data to them. The variables GDB1 through GDB9 and GDB0 are restricted to graph databases; you cannot store another type of data to them. The variables Str1 through Str9 and Str0 are restricted to strings; you cannot store another type of data to them. You can store any string of characters, functions, instructions, or variables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or through the Y= editor. The validity of the string is determined when the function is evaluated. System Variables The variables below must be real numbers. You may store to them. Since the TI.83 can update some of them, as the result of a ZOOM, for example, you may want to avoid using these variables to store nongraphing data. Xmin, Xmax, Xscl, @X, XFact, Tstep, PlotStart, nMin, and other window variables. ZXmin, ZXmax, ZXscl, ZTstep, ZPlotStart, Zu(nMin), and other ZOOM variables. The variables below are reserved for use by the TI.83. You cannot store to them. n, v, Sx, sx, minX, maxX, Gy, Gy2, Gxy, a, b, c, RegEQ, x1, x2, y1, z, t, F, c2, , v1, Sx1, n1, lower, upper, r2, R2 and other statistical variables. Tables and Reference Information A-49 Statistics Formulas This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2.SampTest, and 2.SampTTest. Logistic The logistic regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: J= 1 + ae i =1 N c - bxi 2 - yi which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to estimate the constants a, b, and c recursively to make J as small as possible. SinReg The sine regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: J= [a sin(bx + c) + d - y ] i i i =1 N 2 which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to recursively estimate the constants a, b, c, and d to make J as small as possible. A-50 Tables and Reference Information ANOVA( The ANOVA statistic is: = Factor MS Error MS The mean squares (MS) that make up are: Factor MS = Error MS = Factor SS Factor df Error SS Error df The sum of squares (SS) that make up the mean squares are: Factor SS = n (x - x) i i i =1 I i i =1 I 2 Error SS = (n - 1)Sx 2 i The degrees of freedom df that make up the mean squares are: Factor df = I - 1 = numerator df for Error df = (n - 1) = denominator df for i i =1 I where: I xi Sxi ni x = = = = = number of populations the mean of each list the standard deviation of each list the length of each list the mean of all lists Tables and Reference Information A-51 2-SampTest Below is the definition for the 2.SampTest. Sx1, Sx2 = Sample standard deviations having n1-1 and n2-1 degrees of freedom df, respectively. Sx1 2 = -statistic = Sx 2 df(x, n1-1, n2-1) = pdf( ) with degrees of freedom df, n1-1, and n2-1 p = reported p value 2.SampTest for the alternative hypothesis s 1 > s 2. p= f (x, n - 1, n 1 F F 2 - 1)dx 2.SampTest for the alternative hypothesis s 1 < s 2. p= f (x, n - 1, n 1 0 2 - 1)dx 2.SampTest for the alternative hypothesis s 1 s 2. Limits must satisfy the following: p = 2 Lbnd f ( x , n1 - 1, n2 - 1)dx = 0 Ubnd f (x, n - 1, n 1 2 - 1)dx where: [Lbnd,Ubnd] = lower and upper limits The -statistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral's equality relationship. A-52 Tables and Reference Information 2-SampTTest The following is the definition for the 2.SampTTest. The two-sample t statistic with degrees of freedom df is: t= x1 - x 2 S where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: S= Sx12 Sx22 + n1 n2 Sx12 Sx22 2 + n1 n2 df = 1 Sx12 2 1 Sx 22 2 + n1 - 1 n1 n2 - 1 n2 otherwise: Sxp = ( n1 - 1) Sx12 + ( n2 - 1) Sx22 df 1 1 Sxp + n1 n2 S= df = n1 + n2 - 2 and Sxp is the pooled variance. Tables and Reference Information A-53 Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money i = [e ( y ln( x + 1))] - 1 where: PMT y x C/Y P/Y I% 0 = C/Y P/Y = (.01 I%) C/Y = compounding periods per year = payment periods per year = interest rate per year i = ( - FV PV )(1 N ) - 1 where: PMT = 0 The iteration used to compute i: 1 - (1 + i) 0 = PV + PMT Gi i -N -N + FV (1 + i) I % = 100 C / Y [e ( y ln( x + 1)) - 1] where: x =i y = P/Y C/Y Gi = 1 + i k where: k = 0 for end-of-period payments k = 1 for beginning-of-period payments PMT Gi - FV i ln PMT Gi + PV i N= ln(1 + i) where: i 0 N = -( PV + FV ) PMT where: i =0 A-54 Tables and Reference Information PMT = where: -i PV + FV PV + Gi (1 + i) N - 1 i 0 PMT = -( PV + FV ) N where: i =0 PMT Gi 1 PMT Gi PV = - FV - i i (1 + i) N where: i 0 PV = -( FV + PMT N ) where: i =0 FV = PMT Gi PMT Gi - ( 1 + i )N PV + i i i 0 where: FV = -( PV + PMT N ) where: i =0 Tables and Reference Information A-55 Amortization If computing bal( ), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 Im = RND[ RND12(- i bal( m - 1))] bal( m) = bal (m - 1) - Im + RND( PMT ) then: bal( ) = bal( pmt 2) Pr n ( ) = bal( pmt 2) - bal( pmt1) Int( ) = ( pmt 2 - pmt1 + 1) RND( PMT ) - Pr n ( ) where: RND = round the display to the number of decimal places selected RND12 = round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, , and pmt1 and pmt2. A-56 Tables and Reference Information Cash Flow npv( ) = CF0 + CF (1 + i) j j =1 N - Sj - 1 (1 - (1 + i) i -n j ) j ni where: Sj = i =1 0 j 1 j=0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). irr( ) = 100 i, where i satisfies npv( ) = 0 Internal rate of return is dependent on the values of the initial cash flow (CF0) and subsequent cash flows (CFj). i = I% 100 Interest Rate Conversions 4Eff( ) = 100 (e CP ln( x + 1) - 1) where: x = .01 NOM CP 4Nom( ) = 100 CP [e1 CP ln( x + 1) - 1] where: x EFF CP NOM = = = = .01 EFF effective rate compounding periods nominal rate Tables and Reference Information A-57 Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049. Actual/actual day-count method (assumes actual number of days per month and actual number of days per year): dbd( (days between dates) = Number of Days II - Number of Days I Number of Days I = (Y1-YB) 365 + (number of days MB to M1) + DT1 (Y 1 - YB ) + 4 Number of Days II = (Y2-YB) 365 + (number of days MB to M2) + DT2 (Y 2 - YB ) + 4 where: M1 DT1 Y1 M2 DT2 Y2 MB DB YB = = = = = = = = = month of first date day of first date year of first date month of second date day of second date year of second date base month (January) base day (1) base year (first year after leap year) A-58 Tables and Reference Information B Contents General Information Battery Information ...................................... B-2 In Case of Difficulty ..................................... B-4 Error Conditions ......................................... B-5 Accuracy Information.................................... B-10 Support and Service Information......................... B-12 Warranty Information .................................... B-13 General Information B-1 Battery Information When to Replace the Batteries The TI.83 uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries. When the battery voltage level drops below a usable level, the TI.83 displays this message when you turn on the unit. After this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This one-week to two-week period is based on tests with alkaline batteries; the performance of other kinds of batteries may vary.) The low-battery message continues to be displayed each time you turn on the unit until you replace the batteries. If you do not replace the batteries within about two weeks, the calculator may turn off by itself or fail to turn on until you install new batteries. Replace the lithium battery every three or four years. Effects of Replacing the Batteries Do not remove both types of batteries (AAA and lithium auxiliary) at the same time. Do not allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries on page B.3, you can replace either type of battery without losing any information in memory. Take these precautions when replacing batteries. Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. Do not mix rechargeable and nonrechargeable batteries. Install batteries according to polarity (+ and N) diagrams. Do not place nonrechargeable batteries in a battery recharger. Properly dispose of used batteries immediately. Do not leave them within the reach of children. Do not incinerate batteries. Battery Precautions B-2 General Information Replacing the Batteries To replace the batteries, follow these steps. 1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. 2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover. Push down and toward you to slide the cover about inch (6 mm). Lift off the cover to expose the battery compartment. Note: To avoid loss of information stored in memory, you must turn off the calculator. Do not remove the AAA batteries and the lithium battery simultaneously. 3. Replace all four AAA alkaline batteries at the same time. Or, replace the lithium battery. To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagrams in the battery compartment. To remove the lithium battery, place your index finger on the battery. Insert the tip of a ball-point pen (or similar instrument) under the battery at the small opening provided in the battery compartment. Carefully pry the battery upward, holding it with your thumb and finger. (There is a spring that pushes against the underside of the battery.) Install the new battery, + side up, by inserting the battery and gently snapping it in with your finger. Use a CR1616 or CR1620 (or equivalent) lithium battery. 4. Replace the battery compartment cover. Turn the calculator on and adjust the display contrast, if necessary (step 1; page B.4). General Information B-3 In Case of Difficulty Handling a Difficulty To handle a difficulty, follow these steps. 1. If you cannot see anything on the screen, the contrast may need to be adjusted. To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. To lighten the screen, press and release y, and then press and hold until the display is sufficiently light. 2. If an error menu is displayed, follow the steps in Chapter 1. Refer to pages B.5 through B.9 for details about specific errors, if necessary. 3. If a checkerboard cursor ( # ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full, press y [MEM] 2 to select 2:Delete, and then delete some items from memory (Chapter 18). 4. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI.83 is waiting for input. Press to continue or press to break. 5. If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly. Refer to battery information on pages B.2 and B.3. B-4 General Information Error Conditions When the TI.83 detects an error, it displays ERR:message and an error menu. Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction. Error Type ARCHIVED VAR Possible Causes and Suggested Remedies ARGUMENT BAD GUESS BOUND A function or instruction is archived and therefore cannot be executed or edited. Use the unarchive command to unarchive the variable before using it. A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter. In a CALC operation, you specified a Guess that is not between Left Bound and Right Bound. For the solve( function or the equation solver, you specified a guess that is not between lower and upper. Your guess and several points around it are undefined. Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess. In a CALC operation or with Select(, you defined Left Bound > Right Bound. In fMin(, fMax(, solve(, or the equation solver, you entered lower , upper. You pressed the key to break execution of a program, to halt a DRAW instruction, or to stop evaluation of an expression. You entered a value or variable that is the wrong data type. For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter. In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter. You attempted to store to an incorrect data type, such as a matrix, to a list. You attempted to perform an operation that references more than one list or matrix, but the dimensions do not match. You attempted to divide by zero. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. You attempted a linear regression with a vertical line. BREAK DATA TYPE DIM MISMATCH DIVIDE BY 0 General Information B-5 Error Type DOMAIN Possible Causes and Suggested Remedies You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. See Appendix A and the appropriate chapter. You attempted a logarithmic or power regression with a LX or an exponential or power regression with a LY. You attempted to compute GPrn( or GInt( with pmt2 < pmt1. A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit. The TI.83 was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode. You pressed to break during transmission. You attempted to perform a backup from a TI.82 to a TI.83. You attempted to transfer data (other than L1 through L6) from a TI.83 to a TI.82. You attempted to transfer L1 through L6 from a TI.83 to a TI.82 without using 5:Lists to TI82 on the LINK SEND menu. You attempted to use an invalid function in an argument to a function, such as seq( within expression for seq(. The increment in seq( is 0 or has the wrong sign. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. The increment in a For( loop is 0. You attempted to reference a variable or use a function where it is not valid. For example, Yn cannot reference Y, Xmin, @X, or TblStart. You attempted to reference a variable or function that was transferred from the TI.82 and is not valid for the TI.83. For example, you may have transferred UnN1 to the TI.83 from the TI.82 and then tried to reference it. In Seq mode, you attempted to graph a phase plot without defining both equations of the phase plot. Duplicate Name Error in Xmit ILLEGAL NEST INCREMENT INVALID B-6 General Information Error Type INVALID (cont.) Possible Causes and Suggested Remedies In Seq mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions. In Seq mode, you attempted to reference terms other than (nN1) or (nN2). You attempted to designate a graph style that is invalid within the current graph mode. You attempted to use Select( without having selected (turned on) at least one xyLine or scatter plot. You specified dimensions for an argument that are not appropriate for the operation. You specified a list dimension as something other than an integer between 1 and 999. You specified a matrix dimension as something other than an integer between 1 and 99. You attempted to invert a matrix that is not square. The solve( function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both. irr( has exceeded the maximum number of permitted iterations. When computing , the maximum number of iterations was exceeded. The label in the Goto instruction is not defined with a Lbl instruction in the program. Memory is insufficient to perform the instruction or function. You must delete items from memory (Chapter 18) before executing the instruction or function. Recursive problems return this error; for example, graphing the equation Y1=Y1. Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the End statement that terminates the loop is never reached. INVALID DIM ITERATIONS LABEL MEMORY General Information B-7 Error Type MemoryFull Possible Causes and Suggested Remedies You are unable to transmit an item because the receiving unit's available memory is insufficient. You may skip the item or exit receive mode. During a memory backup, the receiving unit's available memory is insufficient to receive all items in the sending unit's memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again. You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, DrawInv in a graphing mode other than Func. The solve( function or the equation solver did not detect a sign change. You attempted to compute when FV, (PMT), and PV are all , 0, or when FV, (PMT), and PV are all 0. You attempted to compute irr( when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0. In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. You attempted to use a system variable inappropriately. See Appendix A. A singular matrix (determinant = 0) is not valid as the argument for L1. The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. MODE NO SIGN CHNG NONREAL ANS OVERFLOW RESERVED SINGULAR MAT B-8 General Information Error Type SINGULARITY Possible Causes and Suggested Remedies expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both. You attempted a stat calculation with lists that are not appropriate. Statistical analyses must have at least two data points. Med.Med must have at least three points in each partition. When you use a frequency list, its elements must be , 0. (Xmax N Xmin) Xscl must be 47 for a histogram. You attempted to display a graph when a stat plot that uses an undefined list is turned on. The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix A and the appropriate chapter. You requested a tolerance to which the algorithm cannot return an accurate result. You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a after Med.Med. A problem exists with the window variables. You defined Xmax Xmin or Ymax Ymin. You defined qmax qmin and qstep > 0 (or vice versa). You attempted to define Tstep=0. You defined Tmax Tmin and Tstep > 0 (or vice versa). Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI.83's numerical range. A point or a line, instead of a box, is defined in ZBox. A ZOOM operation returned a math error. STAT STAT PLOT SYNTAX TOL NOT MET UNDEFINED WINDOW RANGE ZOOM General Information B-9 Accuracy Information Computational Accuracy To maximize accuracy, the TI.83 carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a two-digit exponent. You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent. RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal setting other than Float causes RegEQ results to be rounded and stored with the specified number of decimal places. Graphing Accuracy Xmin is the center of the leftmost pixel, Xmax is the center of the next-to-the-rightmost pixel. (The rightmost pixel is reserved for the busy indicator.) @X is the distance between the centers of two adjacent pixels. In Full screen mode, @X is calculated as (Xmax N Xmin) 94. In G.T split-screen mode, @X is calculated as (Xmax N Xmin) 46. If you enter a value for @X from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + @X ... 94. In G.T split-screen mode, Xmax is calculated as Xmin + @X ... 46. Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. @Y is the distance between the centers of two adjacent pixels. In Full screen mode, @Y is calculated as (Ymax N Ymin) 62. In Horiz split-screen mode, @Y is calculated as (Ymax N Ymin) 30. In G.T split-screen mode, @Y is calculated as (Ymax N Ymin) 50. If you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y ... 62. In Horiz split-screen mode, Ymax is calculated as Ymin + @Y ... 30. In G.T split-screen mode, Ymax is calculated as Ymin + @Y ... 50. B-10 General Information Cursor coordinates are displayed as eight-character numbers (which may include a negative sign, decimal point, and exponent) when Float mode is selected. X and Y are updated with a maximum accuracy of eight digits. minimum and maximum on the CALCULATE menu are calculated with a tolerance of 1EL5; f(x)dx is calculated at 1EL3. Therefore, the result displayed may not be accurate to all eight displayed digits. For most functions, at least five accurate digits exist. For fMin(, fMax(, and fnInt( on the MATH menu and solve( in the CATALOG, the tolerance can be specified. Function Limits Function sin x, cos x, tan x sinL1 x, cosL1 x ln x, log x ex 10x sinh x, cosh x tanh x sinhL1 x coshL1 x tanhL1 x x (real mode) x (complex mode) x! Range of Input Values 0 |x| < 10 12 (radian or degree) L1 x 1 10 L100 < x < 10 100 L10 100 < x 230.25850929940 L10 100 < x < 100 |x| 230.25850929940 |x| < 10 100 |x| < 5 10 99 1 x < 5 10 99 L1 < x < 1 0 x < 10 100 |x| < 10 100 L.5 x 69, where x is a multiple of .5 Range of Result Function Results Function sinL1 x, tanL1 x cosL1 x L90 to 90 or Lp2 to p2 (radians) 0 to 180 or 0 to p (radians) General Information B-11 Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail: 1.800.TI.CARES (1.800.842.2737) ti-cares@ti.com For technical questions, call the Programming Assistance Group of Customer Support: phone: 1.972.917.8324 Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands Contact TI by e-mail or visit the TI calculator home page on the World Wide Web. e-mail: Internet: ti-cares@ti.com education.ti.com Product Service Customers in the U.S. and Canada Only Always contact Texas Instruments Customer Support before returning a product for service. Customers outside the U.S. and Canada Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor. Other TI Products and Services Visit the TI calculator home page on the World Wide Web. education.ti.com Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor. B-12 General Information Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Electronic Product This Texas Instruments ("TI") electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This TI electronic product is warranted against defective materials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR CONSTRUCTION. Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER. Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI's option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. The software and any documentation supplied with this product are protected by copyright. General Information B-13 Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction. Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in duration to the above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or damages incurred by the consumer or any other user. Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI's option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. The software and any documentation supplied with this product are protected by copyright. All Customers Outside the U.S. and Canada For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor. B-14 General Information Index + (addition), 2-3, A-38 c2cdf( (chi-square cdf), 13-31, A-3 c2pdf( (chi-square pdf), 13-31, A-4 c2.Test (chi-square test), 13-22, A-4 : (colon), 6, 16-5 + (concatenation), 15-6, A-38 3 3( .A. a+bi (rectangular complex mode), = ! > , L1 < {} ' M () p > + ^ 10^( x " 2 ( ! "" N (cube), 2-6, A-35 (cube root), 2-6, A-35 (degrees notation), 2-3, A-34 (division), 2-3, A-37 (equal-to relational test), 2-25, A-35 (factorial), 2-21, A-34 (graph style, animate), 3-9 (graph style, dot), 3-9 (graph style, line), 3-9 (greater than), 2-25, A-35 (greater than or equal to), 2-25, A-35 (inverse), 2-3, 8-9, 10-10, A-36 (less than), 2-25, A-35 (less than or equal to), 2-25, A-36 (list indicator), 11-4 (matrix indicator), 10-7 (minutes notation), 2-23, A-38 (multiplication), 2-3, A-37 (negation), 1-23, 2-4, A-37 (not equal to), 2-25, A-35 (parentheses), 1-23 (pi), 2-4 (pixel mark), 8-15, 12-34 (pixel mark), 8-15, 12-34 (pixel mark), 8-15, 12-34 (plot type, box), 12-33 (plot type, histogram), 12-32 (plot type, modified box), 12-32 (plot type, normal probability), 12-33 (power), 2-3, A-36, A-37 (power of ten), 2-4, A-37 (root), 2-6, A-35 (seconds notation), 2-23, A-38 (square) , 2 - 3 , A-36 (square root) , 2 - 3 , A-37 Store, 1-14, A-28 (string indicator), 15-3 (subtraction), 2-3, A-38 1-12, 2-16, A-3 above graph style(), 3-9 abs( (absolute value), 2-13, 2-19, 10-10, A-2 accuracy information computational and graphing, B-10 graphing, 3-17 function limits and results, B-11 addition (+), 2-3, A-38 alpha cursor, 1-5 alpha key, 3 alpha-lock, 1-8 alternative hypothesis, 13-7 amortization bal( (amortization balance), 14-9, A-3 calculating schedules, 14-9 formula, A-56 GInt( (sum of interest),14.9, A-12 GPrn( (sum of principal), 14-9, A-19 and (Boolean operator), 2-26, A-2 angle(, 2-19, A-2 ANGLE menu, 2-23 angle modes, 1-11 animate graph style (), 3-9 ANOVA( (one-way variance analysis), 13-25, A-2 formula, A-51 Ans (last answer), 1-18, A-2 APD (Automatic Power DownTM), 1-2 applications. See examples, applications arccosine (cosM1(), 2-3 arcsine (sinM1(), 2-3 arctangent (tanM1(), 2-3 augment(, 10-14, 11-15, A-3 Automatic Power DownTM (APD), 1-2 automatic regression equation, 12-22 automatic residual list (RESID), 12-22 axes format, sequence graphing, 6-8 axes, displaying (AxesOn, AxesOff), 3-14, A-3 AxesOff, 3-14, A-3 AxesOn, 3-14, A-3 Index-1 .B. backing up calculator memory, 19-4, 19-10 bal( (amortization balance), 14-9, A-3 batteries, 1-2, B-2 below graph style (), 3-9 binomcdf(, 13-33, A-3 binompdf(, 13-33, A-3 Boolean logic, 2-26 box pixel mark (>), 8-15, 12-34 Boxplot plot type ( ), 12-33 busy indicator, 1-4 . C (continued) . complex modes (a+bi, re^qi), 1-12, 2-16, A-3, A-22 numbers, 1-12, 2-16, 2-18, A-22 compounding-periods-per-year variable (C/Y), 14-4, 14-14 concatenation (+), 15-6, A-38 confidence intervals, 13-8, 13-16 N 13.21 conj( (conjugate), 2-18, A-4 Connected (plotting mode), 1-11, A-4 contrast (display), 1-3 convergence, sequence graphing, 6-12 conversions 4Dec (to decimal), 2-5, A-5 4DMS (to degrees/minutes/ seconds), 2-24, A-7 4Eff (to effective interest rate), 14-12, A-7 Equ4String( (equation-to-string conversion), 15-7, A-8 4Frac (to fraction conversion), 2-5, A-10 List4matr( (list-to-matrix conversion), 10-14, 11-15, A-14 Matr4list( (matrix-to-list conversion), 10-14, 11-16, A-15 4Nom (to nominal interest rate conversion), 14-12, A-16 4Polar (to polar conversion), 2-19, A-19 P4Rx(, P4Ry( (polar-to-rectangular conversion), 2-24, A-21 4Rect (to rectangular conversion), 2-19, A-22 R4Pr(, R4Pq( (rectangular-to-polar conversion), 2-24, A-23 String4Equ( (string-to-equation conversion), 15-8, A-29 CoordOff, 3-14, A-5 CoordOn, 3-14, A-5 correlation coefficient (r), 12-23, 12-25 to 12-27 cos( (cosine), 2-3, A-5 cosM1( (arccosine), 2-3, A-5 cosh( (hyperbolic cosine), 15-10, A-5 .C. CALCULATE menu, 3-25 Calculate output option, 13-6, 13-8 cash flow calculating, 14-8 formula, A-57 irr( (internal rate of return), 14-8, A-13 npv( (net present value), 14-8, A-17 CATALOG, 15-2 CBL 2/CBL System, 16-21, 19-3, A-10 CBR, 16-21, 19-3, A-10 Check RAM (memory screen), 18-2 chi-square cdf (c2cdf(), 13-31, A-3 chi-square pdf (c2pdf(), 13-31, A-4 chi-square test (c2.Test), 13-22, A-4 Circle( (draw circle), 8-11, A-4 Clear Entries, 18-4, A-4 clearing entries (Clear Entries), 18-4, A-4 all lists (ClrAllLists), 18-4, A-4 drawing (ClrDraw), 8-4, A-4 home screen (ClrHome), 16-20, A-4 list (ClrList), 12-20, A-4 table (ClrTable), 16-20, A-4 ClrAllLists (clear all lists), 18-4, A-4 ClrDraw (clear drawing), 8-4, A-4 ClrHome (clear home screen), 16-20, A-4 ClrList (clear list), 12-20, A-4 ClrTable (clear table), 16-20, A-4 coefficients of determination (r2, R2), 12-23 colon separator (:), 6, 16-5 combinations (nCr), 2-21, A-16 Index-2 . D (continued) . coshM1( (hyperbolic arccosine), 15-10, . D (continued) . dimensioning a list or matrix, 10-12, 10-13, 11-11, A-6 dim( (dimension), 10-12, 11-11, A-6 !dim( (assign dimension), 10-13, 11-11, A-6 Disp (display), 16-18, A-6 DispGraph (display graph), 16-19, A-7 display contrast, 1-3 display cursors, 1-5 DispTable (display table), 16-19, A-7 DISTR (distributions menu), 13-29 DISTR DRAW (distributions drawing menu), 13-35 distribution functions binomcdf(, 13-33, A-3 binompdf(, 13-33, A-3 c2cdf(, 13-31, A-3 c2pdf(, 13-31, A-4 cdf(, 13-32, A-8 pdf(, 13-32, A-9 geometcdf(, 13-34, A-10 geometpdf(, 13-34, A-11 invNorm(, 13-30, A-12 normalcdf(, 13-30, A-17 normalpdf(, 13-29, A-17 poissoncdf(, 13-34, A-99 poissonpdf(, 13-33, A-19 tcdf(, 13-31, A-29 tpdf(, 13-30, A-29 distribution shading instructions Shadec2(, 13-36, A-26 Shade(, 13-36, A-27 ShadeNorm(, 13-35, A-27 Shade_t(, 13-36, A-27 division () , 2-3, A-37 DMS (degrees/minutes/seconds entry notation), 2-23, A-38 4DMS (to degrees/minutes/seconds), 2-24, A-7 dot graph style (), 3-9 dot pixel mark (), 8-15, 12-34 Dot (plotting mode), 1-11, A-7 DrawF (draw a function), 8-9, A-7 A-5 cosine (cos(), 2-3, A-5 cross pixel mark (+), 8-15, 12-34 cube ( 3) , 2-6, A-35 cube root (3(), 2-6, A-35 CubicReg (cubic regression), 12-26, A-5 cubic regression (CubicReg), 12-26, A-5 cumulative sum (cumSum(), 10-15, 11-12, A-5 cumSum( (cumulative sum), 10-15, 11-12, A-5 cursors, 1-5, 1-8 C/Y (compounding-periods-per-year variable), 14-4, 14-14 .D. Data input option, 13-6, 13-7 days between dates (dbd(), 14-13, A-5, A-58 dbd( (days between dates), 14-13, A-5, A-58 4Dec (to decimal conversion), 2-5, A-5 decimal mode (float or fixed), 1-10 decrement and skip (DS<(), 16-14, A-7 definite integral, 2-7, 3-28, 4-8, 5-6 Degree angle mode, 1-11, 2-23, A-6 degrees notation ( ) , 2-3, A-34 DELETE FROM menu, 18-3 delete variable contents (DelVar), 16-15, A-6 DelVar (delete variable contents), 16-15, A-6 DependAsk, 7-3, 7-5, A-6 DependAuto, 7-3, 7-5, A-6 derivative. See numerical derivative det( (determinant), 10-12, A-6 determinant (det(), 10-12, A-6 DiagnosticOff, 12-23, A-6 DiagnosticOn, 12-23, A-6 diagnostics display mode(r, r2, R2), 12-23 differentiation, 2-8, 3-28, 4-8, 5-6 Index-3 . D (continued) . drawing on a graph circles (Circle(), 8-11 functions and inverses (DrawF, DrawInv), 8-9 lines (Horizontal, Line(, Vertical), 8-6, 8-7 line segments (Line(), 8-5 pixels (Pxl.Change, Pxl.Off, Pxl.On, pxl.Test), 8-16 points (Pt.Change, Pt.Off, Pt.On), 8-14 tangents (Tangent), 8-8 text (Text), 8-12 using Pen, 8-13 DrawInv (draw inverse), 8-9, A-7 DRAW menu, 8-3 DRAW instructions, 8-3 N 8.16 Draw output option, 13-6 N 13.8 DRAW POINTS menu, 8-14 DRAW STO (draw store menu), 8-17 dr/dq operation on a graph, 5-6 DS<( (decrement and skip), 16-14, A-7 DuplicateName menu, 19-5 dx/dt operation on a graph, 3-28, 4-8 dy/dx operation on a graph, 3-28, 4-8, 5-6 . E (continued) . Equ4String( (equation-to-string .E. e (constant), 2-4 e^( (exponential), 2-4, A-7 (exponent), 1-7, 1-10, A-7 edit keys table, 1-8 4Eff( (to effective interest rate), 14-12, A-7 Else, 16-10 End, 16-12, A-8 Eng (engineering notation mode), 1-10, A-8 entry cursor, 1-5 ENTRY (last entry key), 1-16 EOS (Equation Operating System), 1-22 eqn (equation variable), 2-8, 2-12 equal-to relational test (=), 2-25, A-35 Equation Operating System (EOS), 1-22 Equation Solver, 2-8 equations with multiple roots, 2-12 conversion), 15-7, A-8 errors diagnosing and correcting, 1-24 messages, B-5 examples--applications area between curves, 17-11 areas of regular n-sided polygons, 17-16 box plots, 17-2 cobweb attractors, 17-8 fundamental theorem of calculus, 17-14 guess the coefficients, 17-9 inequalities, 17-5 mortgage payments 17.18 parametric equations: ferris wheel problem, 17-12 piecewise functions, 17-4 Sierpinski triangle, 17-7 solving a system of nonlinear equations, 17-6 unit circle and trig curves, 17-10 examples--Getting Started box with lid 9 to 16 defining a, 9 defining a table of values, 10 finding calculated maximum, 16 setting the viewing window, 12 tracing the graph, 13 zooming in on the graph, 15 zooming in on the table, 11 coin flip, 2-2 compound interest, 14-3 drawing a tangent line, 8-2 financing a car, 14-2 forest and trees, 6-2 generating a sequence, 11-2 graphing a circle, 3-2 mean height of a population, 13-2 path of a ball, 4-2 pendulum lengths and periods, 12-2 polar rose, 5-2 Index-4 . E (continued) . examples--Getting Started (continued) quadratic formula converting to a fraction, 7 displaying complex results, 8 entering a calculation, 6 roots of a, 7-2 sending variables, 19-2 solving a system of linear equations, 10-2 unit circle, 9-2 volume of a cylinder, 16-2 examples--miscellaneous convergence, 6-12 daylight hours in Alaska, 12-28 calculating outstanding loan balances, 14-10 predator-prey model, 6-13 exponential regression (ExpReg), 12-26, A-8 expr( (string-to-expression conversion), 15-7, A-8 ExpReg (exponential regression), 12-26, A-8 expression, 1-6 converting from string (expr(), 15-7, A-8 turning on and off (ExprOn, ExprOff), 3-14, A-8 ExprOff (expression off), 3-14, A-8 ExprOn (expression on), 3-14, A-8 . F (continued) . Fix (fixed-decimal mode), 1-10, A-8 fixed-decimal mode (Fix), 1-10, A-8 Float (floating-decimal mode), 1-10, A-8 floating-decimal mode (Float), 1-10, A-8 fMax( (function maximum), 2-6, A-9 fMin( (function minimum), 2-6, A-9 fnInt( (function integral), 2-7, A-9 FnOff (function off), 3-8, A-9 FnOn (function on), 3-8, A-9 For(, 16-10, A-9 format settings, 3-13, 6-8 formulas amortization, A-56 ANOVA, A-51 cash flow, A-57 days between dates, A-58 factorial, 2-21 interest rate conversions, A-57 logistic regression, A-50 sine regression, A-50 time value of money, A-54 two-sample -Test, A-52 two-sample t test, A-53 fPart( (fractional part), 2-14, 10-11, A-9 pdf(, 13-32, A-9 4Frac (to fraction), 2-5, A-10 free-moving cursor, 3-17 frequency, 12-24 Full (full-screen mode), 1-12, A-10 full-screen mode (Full), 1-12, A-10 Func (function graphing mode), 1-11, A-10 function, definition of, 1-7 function graphing, 3-1 to 3-28 accuracy, 3-17 CALC (calculate menu), 3-25 defining and displaying, 3-3 defining in the Y= editor, 3-5 defining on the home screen, in a program, 3-6 deselecting, 3-7 displaying, 3-3, 3-11, 3-15 evaluating, 3-6 family of curves, 3-16 format settings, 3-13 .F. f(x)dx operation on a graph, 3-28 factorial (!), 2-21, A-34 family of curves, 3-16 cdf(, 13-32, A-8 Fill(, 10-13, A-8 FINANCE CALC menu, 14-5 FINANCE VARS menu, 14-14 financial functions amortization schedules, 14-9 cash flows, 14-8 days between dates, 14-13 interest rate conversions, 14-12 payment method, 14-13 time value of money (TVM), 14-6 Index-5 . F (continued) . Function graphing (continued) free-moving cursor, 3-17 graph styles, 3-9 maximum of (fMax(), 2-6, A-9 minimum of (fMin(), 2-6, A-9 modes, 1-11, 3-4, A-10 moving the cursor to a value, 3-19 overlaying functions on a graph, 3-16 panning, 3-19 pausing or stopping a graph, 3-15 Quick Zoom, 3-19 selecting, 3-7, 3-8, A-9 shading, 3-10 Smart Graph, 3-15 tracing, 3-18 window variables, 3-11, 3-12 Y= editor, 3-5 viewing window, 3-11 @X and @Y window variables, 3-12 ZOOM menu, 3-20 ZOOM MEMORY menu, 3-23 function integral (fnInt(), 2-7, A-9 functions and instructions table, A-2 to A-2 future value, 14-5, 14-7, 14-14 present value, 14-5, 14-7, 14-14 FV (future-value variable), 14-4, 14-14 . G (continued) . graph database (GDB), 8-19 graphing modes, 1-11 graphing-order modes, 1-12 GraphStyle(, 16-15, A-11 graph styles, 3-9 graph-table split-screen mode (G.T), 1-12, 9-5, A-11 greater than (>), 2-25, A-35 greater than or equal to (,), 2-25, A-35 greatest common divisor (gcd(), 2-15, A-10 greatest integer (int(), 2-14, 10-11, A-12 GridOff, 3-14, A-11 GridOn, 3-14, A-11 G.T (graph-table split-screen mode), 1-12, 9-5, A-11 .H. Histogram plot type (), 12-32 home screen, 1-4 Horiz (horizontal split-screen mode), 1-12, 9-4, A-11 hyperbolic functions, 15-10 Horizontal (draw line), 8-6 N 8.7, A-11 hypothesis tests, 13-10 N 13.15 .I. i (complex number constant), 2-17 (annual interest rate variable), 14-4, 14-14 identity(, 10-13, A-11 If instructions If, 16-9, A-11 If-Then, 16-9, A-11 If-Then-Else, 16-10, A-11 imag( (imaginary part), 2-18, A-11 imaginary part (imag(), 2-18, A-11 implied multiplication, 1-23 increment and skip (IS>(), 16-13, A-13 IndpntAsk, 7-3, A-12 IndpntAuto, 7-3, A-12 independent variable, 7-3, A-12 inferential stat editors, 13-6 .G . gcd( (greatest common divisor), 2-15, A-10 GDB (graph database), 8-19 geometcdf(, 13-34, A-10 geometpdf(, 13-34, A-10 Get( (get data from CBL 2/CBL or CBR), 16-21, A-10 GetCalc( (get data from TI.83), 16-21, A-10 getKey, 16-20, A-10 Getting Started, 1 to 18. See also examples, Getting Started Goto, 16-13, A-10 Index-6 . I (continued) . inferential statistics. See also stat tests; confidence intervals alternative hypotheses, 13-7 bypassing editors, 13-8 calculating test results (Calculate), 13-8 confidence interval calculations, 13-8, 13-16 N 13.21 data input or stats input, 13-7 entering argument values, 13-7 graphing test results (Draw), 13-8 input descriptions table, 13-26 pooled option, 13-8 STAT TESTS menu, 13-9 test and interval output variables, 13-28 Input, 16-16, 16-17, A-12 insert cursor, 1-5 inString( (in string), 15-7, A-12 instruction, definition of, 1-7 int( (greatest integer), 2-14, 10-11, A-12 GInt( (sum of interest), 14-9, A-12 integer part (iPart(), 2-14, 10-11, A-12 integral. See numerical integral interest rate conversions calculating, 14-12 4Eff( (compute effective interest rate), 14-12, A-7 formula, A-57 4Nom( (compute nominal interest rate), 14-12, A-16 internal rate of return (irr(), 14-8, A-13 intersect operation on a graph, 3-27 inverse (L1), 2-3, 8-9, 10-10, A-36 inverse cumulative normal distribution (invNorm(), 13-30, A-12 inverse trig functions, 2-3 invNorm( (inverse cumulative normal distribution), 13-30, A-12 iPart( (integer part), 2-14, 10-11, A-12 irr( (internal rate of return), 14-8, A-13 IS>( (increment and skip), 16-13, A-13 .K. keyboard layout, 2, 3 math operations, 2-3 key-code diagram, 16-20 .L. (user-created list name symbol), 11-16, A-13 LabelOff, 3-14, A-13 LabelOn, 3-14, A-13 labels graph, 3-14, A-13 program, 16-13, A-13 Last Entry, 1-16 Lbl (label), 16-13, A-13 lcm( (least common multiple), 2-15, A-13 least common multiple (lcm(), 2-15, A-13 length( of string, 15-8, A-13 less than (<), 2-25, A-35 less than or equal to (), 2-25, A-36 line graph style (), 3-9 Line( (draw line), 8-5, A-13 line segments, drawing, 8-5 lines, drawing, 8-6, 8-7 linking receiving items, 19-5 to a CBL 2/CBL System or CBR, 19-3 to a PC or Macintosh, 19-3 to a TI.82, 19-3, 19-8 transmitting items, 19-6 two TI.83 units, 19-3 LINK RECEIVE menu, 19-5 LINK SEND menu, 19-4 LinReg(a+bx) (linear regression), 12-26, A-14 LinReg(ax+b) (linear regression), 12-25, A-14 LinRegTTest (linear regression t test), 13-24, A-14 @List(, 11-12, A-14 LIST MATH menu, 11-17 List4matr( (lists-to-matrix conversion), 10-14, 11-15, A-14 LIST NAMES menu, 11-6 LIST OPS menu, 11-10 L Index-7 . L (continued) . lists, 11-1 to 11-18 accessing an element, 11-5 attaching formulas, 11-7, 12-14 clearing all elements, 12-12, 12-20 copying, 11-5 creating, 11-3, 12-12 deleting from memory, 11-5, 18-3 detaching formulas, 11-8, 12-16 dimension, 11-4, 11-11 entering list names, 11-6, 12-11 indicator ({ }), 11-4 naming lists, 11-3 storing and displaying, 11-4 transmitting to and from TI.82, 19-4 using in expressions, 11-9 using to graph a family of curves, 3-16, 11-5 using to select data points from a plot, 11-13 using with math functions, 11-9 using with math operations, 2-3 ln(, 2-4, A-14 LnReg (logarithmic regression), 12-26, A-14 log(, 2-4, A-14 logic (Boolean) operators, 2-26 Logistic (regression), 12-27, A-15 logistic regression formula, A-50 . M (continued) . matrices, (continued) indicator ([ ]), 10-7 inverse (L1), 10-10 math functions, 10-9 to 10-11 matrix math functions (det(, T, dim(, Fill(, identity(, randM(, augment(, Matr4list(, List4matr(, cumSum(), 10-12 to 10-16 referencing in expressions, 10-7 relational operations, 10-11 row operations(ref(, rref(, rowSwap(, row+(, row(, row+( ), 10-15 selecting, 10-3 viewing, 10-5 MATRX EDIT menu, 10-3 MATRX MATH menu, 10-12 MATRX NAMES menu, 10-7 max( (maximum), 2-15, 11-17, A-15 maximum of a function (fMax(), 2-6, A-9 maximum operation on a graph, 3-27 mean(, 11-17, A-15 median(, 11-17, A-15 Med.Med (median-median), 12-25, A-15 memory backing up, 19-10 checking available, 18-2 clearing all list elements from, 18-4 clearing entries from, 18-4 deleting items from, 18-3 insufficient during transmission, 19-5 resetting defaults, 18-6 resetting memory, 18-5 MEMORY menu, 18-2 Menu( (define menu), 16-14, A-15 menus, 4, 1-19 defining (Menu(), 16-14, A-15 map, A-39 scrolling, 1-19 min( (minimum), 2-15, 11-17, A-16 minimum operation on a graph, 3-27 minimum of a function (fMin(), 2-6, A-9 minutes notation ( ') , 2-23, A-38 ModBoxplot plot type (), 12-32 .M. MATH CPX (complex menu), 2-18 MATH menu, 2-5 MATH NUM (number menu), 2-13 math operations, keyboard, 2-3 MATH PRB (probability menu), 2-20 Matr4list( (matrix-to-list conversion), 10-14, 11-16, A-15 matrices, 10-1 to 10.16 accessing elements, 10-8 copying, 10-8 defined, 10-3 deleting from memory, 10-4 dimensions, 10-3, 10-12, 10-13 displaying a matrix, 10-8 displaying matrix elements, 10-4 editing matrix elements, 10-6 Index-8 . M (continued) . modified box plot type (), 12-32 mode settings, 1-9 a+bi (complex rectangular), 1-12, 2-16, A-3 re^qi (complex polar), 1-12, 2-16, A-22 Connected (plotting), 1-11, A-4 Degree (angle), 1-11, 2-24, A-6 Dot (plotting), 1-11, A-7 Eng (notation), 1-10, A-8 Fix (decimal), 1-10, A-8 Float (decimal), 1-10, A-8 Full (screen), 1-12, A-10 Func (graphing), 1-11, A-10 G.T (screen), 1-12, A-11 Horiz (screen), 1-12, A-11 Normal (notation), 1-10, A-16 Par/Param (graphing), 1-11, A-18 Pol/Polar (graphing), 1-11, A-19 Radian (angle), 1-11, 2-24, A-21 Real, 1-12, A-22 Sci (notation), 1-10, A-25 Seq (graphing), 1-11, A-26 Sequential (graphing order), 1-12, A-26 Simul (graphing order), 1-12, A-27 modified box plot type (), 12-32 multiple entries on a line, 1-6 multiplication (), 2-3, A-37 multiplicative inverse, 2-3 . N (continued) . normalcdf( (normal distribution probability), 13-30, A-17 normalpdf( (probability density function), 13-29, A-17 NormProbPlot plot type (), 12-33 not( (Boolean operator), 2-26, A-17 not equal to (), 2-25, A-35 nPr (permutations), 2-21, A-17 npv( (net present value), 14-8, A-17 numerical derivative, 2-7, 3-28, 4-8, 5-6 numerical integral, 2-7, 3-28 .O. one-proportion z confidence interval (1.PropZInt), 13-20, A-20 one-proportion z test (1.PropZTest), 13-14, A-20 one-sample t confidence interval (TInterval), 13-17, A-30 one-variable statistics (1.Var Stats), 12-25, A-31 or (Boolean) operator, 2-26, A-17 order of evaluating equations, 1-22 Output(, 9-6, 16-19, A-18 .P. panning, 3-19 Par/Param (parametric graphing mode), 1-9, 1-11, A-18 parametric equations, 4-5 parametric graphing CALC (calculate operations on a graph), 4-8 defining and editing, 4-4 free-moving cursor, 4-7 graph format, 4-6 graph styles, 4-4 moving the cursor to a value, 4-8 selecting and deselecting, 4-5 setting parametric mode, 4-4 tracing, 4-7 window variables, 4-5 Y= editor, 4-4 zoom operations, 4-8 parentheses, 1-23 path () graph style, 3-9 .N. (number of payment periods variable), 14-4, 14-14 nCr (number of combinations), 2-21, A-16 nDeriv( (numerical derivative), 2-7, A-16 negation (M), 1-23, 2-4, A-37 4Nom( (to nominal interest rate), 14-12, A-16 nonrecursive sequences, 6-5 normal distribution probability (normalcdf(), 13-30, A-17 Normal notation mode, 1-10, A-16 normal probability plot type (), 12-33 Index-9 . P (continued) . Pause, 16-12, A-18 pausing a graph, 3-15 Pen, 8-13 permutations (nPr), 2-21, A-17 phase plots, 6-13 Pi (p), 2-4 Pic (pictures), 8-17, 8-18 pictures (Pic), 8-17, 8-18 pixel, 8-16 pixels in Horiz/G.T modes, 8-16, 9-6 Plot1(, 12-34, A-18 Plot2(, 12-34, A-18 Plot3(, 12-34, A-18 PlotsOff, 12-35, A-18 PlotsOn, 12-35, A-18 plotting modes, 1-11 plotting stat data, 12-31 PMT (payment amount variable), 14-4, 14-14 Pmt_Bgn (payment beginning variable), 14-13, A-19 Pmt_End (payment end variable), 14-13, A-19 poissoncdf(, 13-34, A-19 poissonpdf(, 13-33, A-19 Pol/Polar (polar graphing mode), 1-9, 1-11, A-19 polar equations, 5-4 polar form, complex numbers, 2-17 4Polar (to polar), 2-19, A-19 polar graphing CALC (calculate operations on a graph), 5-6 defining and displaying, 5-3 equations, 5-4 free-moving cursor, 5-6 graph format, 5-5 graph styles, 5-3 moving the cursor to a value, 5-6 selecting and deselecting, 5-4 mode (Pol/Polar), 1-9, 1-11, 5-3, A-19 tracing, 5-6 window variables, 5-4 Y= editor, 5-3 ZOOM operations, 5-6 PolarGC (polar graphing coordinates), 3-13, A-19 . P (continued) . pooled option, 13-6, 13-8 power (^), 2-3, A-36, A-37 power of ten (10^(), 2-4, A-37 present value, 14-5, 14-7, 14-14 previous entry (Last Entry), 1-16 PRGM CTL (program control menu), 16-8 PRGM EDIT menu, 16-7 PRGM EXEC menu, 16-7 PRGM I/O (Input/Output menu), 16-16 prgm (program name), 16-15, A-19 PRGM NEW menu, 16-4 GPrn( (sum of principal), 14-9, A-19 probability, 2-20 probability density function (normalpdf(), 13-29, A-17 prod( (product), 11-18, A-19 programming copying and renaming, 16-7 creating new, 16-4 defined, 16-4 deleting, 16-4 deleting command lines, 16-6 editing, 16-6 entering command lines, 16-5 executing, 16-5 instructions, 16-9 N 16.21 inserting command lines, 16-6 name (prgm), 16-15, A-19 renaming, 16-7 stopping, 16-5 subroutines, 16-22 Prompt, 16-18, A-19 1.PropZInt (one-proportion z confidence interval), 13-20, A-20 1.PropZTest (one-proportion z test), 13-14, A-20 2.PropZInt (two-proportion z confidence interval), 13-21, A-20 2.PropZTest (two-proportion z test), 13-15, A-20 P4Rx(, P4Ry( (polar-to-rectangular conversions), 2-24, A-21 Pt.Change(, 8-15, A-20 Pt.Off(, 8-15, A-20 Pt.On(, 8-14, A-20 Index-10 . P (continued) . PV (present value variable), 14-4, . R (continued) . RegEQ (regression equation variable), 14-14 p-value, 13-28 PwrReg (power regression), 12-27, A-20 Pxl.Change(, 8-16, A-21 Pxl.Off(, 8-16, A-21 Pxl.On(, 8-16, A-21 pxl.Test(, 8-16, A-21 P/Y (number-of-payment-periods-peryear variable), 14-4, 14-14 .Q. QuadReg (quadratic regression), 12-25, A-21 QuartReg (quartic regression), 12-26 Quick Zoom, 3-19, A-21 .R. r (radian notation), 2-24, A-34 r (correlation coefficient), 12-23 r2, R2 (coefficients of determination), 12-23 Radian angle mode, 1-11, 2-24, A-21 radian notation (r), 2-24, A-34 rand (random number), 2-20, A-21 randBin( (random binomial), 2-22, A-21 randInt( (random integer), 2-22, A-22 randM( (random matrix), 10-13, A-22 randNorm( (random Normal), 2-22, 12-22, 12-29 regression model automatic regression equation, 12-22 automatic residual list feature, 12-22 diagnostics display mode, 12-23 models, 12-25 relational operations, 2-25, 10-11 Repeat, 16-11, A-23 RESET menu, 18-5 resetting defaults, 18-6 memory, 5, 18-5 residual list (RESID), 12-22 Return, 16-15, A-23 root (x), 2-6, A-35 root of a function, 3-26 round(, 2-13, 10-10, A-23 row+(, 10-16, A-23 ...row(, 10-16, A-23 ...row+(, 10-16, A-23 rowSwap(, 10-16, A-23 R4Pr(, R4Pq( (rectangular-to-polar conversions), 2-24, A-23 rref( (reduced-row-echelon form), 10-15, A-23 .S. 2.SampTest (two-sample -Test), A-22 random seed, 2-20, 2-22 RCL (recall), 1-15, 11-9 re^qi (polar complex mode), 1-12, 2-16, A-22 Real mode, 1-12, A-22 real( (real part), 2-18, A-22 RecallGDB, 8-20, A-22 RecallPic, 8-18, A-22 4Rect (to rectangular), 2-19, A-22 rectangular form, complex numbers, 2-17 RectGC (rectangular graphing coordinates), 3-13, A-22 recursive sequences, 6-6 ref( (row-echelon form), 10-15, A-22 13-23, A-24 2.SampTInt (two-sample t confidence interval), 13-19, A-24 2.SampTTest (two-sample t test), 13-13, A-24, A-25 2.SampZInt (two-sample z confidence interval), 13-18, A-25 2.SampZTest (two-sample z test), 13-12, A-25 Scatter plot type ("), 12-31 Sci (scientific notation mode), 1-10, A-25 scientific notation, 1-7,1.10 screen modes, 1-12 second cursor (2nd), 1-5 second key (2nd), 3 Index-11 . S (continued) . seconds DMS notation ( ") , 2-23 Select(, 11-12, A-25 selecting data points from a plot, 11-13 functions from the home screen or a program, 3-8 functions in the Y= editor, 3-7 items from menus, 4 stat plots from the Y= editor, 3-7 Send( (send to CBL 2/CBL or CBR), 16-21, A-26 sending. See transmitting Seq (sequence graphing mode), 1-11, A-26 seq( (sequence), 11-12, A-26 sequence graphing axes format, 6-8 CALC (calculate menu), 6-10 defining and displaying, 6-3 evaluating, 6-10 free-moving cursor, 6-9 graph format, 6-8 graph styles, 6-4 moving the cursor to a value, 6-9 nonrecursive sequences, 6-5 phase plots, 6-13 recursive sequences, 6-6 setting sequence mode, 6-3 selecting and deselecting, 6-4 TI.83 versus TI.82 table, 6-15 tracing, 6-9 web plots, 6-11 window variables, 6-7 Y= editor, 6-4 ZOOM (zoom menu), 6-10 Sequential (graphing order mode), 1-12, A-26 service information, B-12 setting display contrast, 1-3 graph styles, 3-9 graph styles from a program, 3-10 modes, 1-9 modes from a program, 1-9 split-screen modes, 9-3 split-screen modes from a program, 9-6 tables from a program, 7-3 . S (continued) . SetUpEditor, 12-21, A-26 shade above () graph style, 3-9 shade below () graph style, 3-10 Shade(, 8-9, A-26 Shadec2(, 13-36, A-26 Shade(, 13-36, A-27 ShadeNorm(, 13-35, A-27 Shade_t(, 13-36, A-27 shading graph areas, 3-10, 8-10 Simul (simultaneous graphing order mode), 1-12, A-27 sin( (sine), 2-3, A-27 sinM1( (arcsine), 2-3, A-27 sine (sin(), 2-3, A-27 sine regression formula, A-50 sinh( (hyperbolic sine), 15-10, A-27 sinhM1( (hyperbolic arcsine), 15-10, A-27 SinReg (sinusoidal regression), 12-27, A-28 Smart Graph, 3-15 solve(, 2-12, A-28 Solver, 2-8 solving for variables in the equation solver, 2-10, 2-11 SortA( (sort ascending), 11-10, 12-20, A-28 SortD( (sort descending), 11-10, 12-20, A-28 split-screen modes G.T (graph-table) mode, 9-5 Horiz (horizontal) mode, 9-4 setting, 9-3, 9-6 split-screen values, 8-12, 8-16, 9-6 square ( 2) , 2 - 3 , A-36 square root (() , 2 - 3 , A-37 STAT CALC menu, 12-24 STAT EDIT menu, 12-20 stat list editor attaching formulas to list names, 12-14 clearing elements from lists, 12-12 creating list names, 12-12 detaching formulas from list names, 12-16 displaying, 12-10 edit-elements context, 12-18 Index-12 . S (continued) . stat list editor (continued) editing elements of formulagenerated lists, 12-16 editing list elements, 12-13 enter-names context, 12-19 entering list names, 12-11 formula-generated list names, 12-15 removing lists, 12-12 restoring list names L1L6, 12-12, 12-21 switching contexts, 12-17 view-elements context, 12-18 view-names context, 12-19 STAT PLOTS menu, 12-34 stat tests and confidence intervals ANOVA( (one-way analysis of variance), 13-25 c.Test (chi-square test), 13-22 LinRegTTest (linear regression t test), 13-24 1.PropZInt (one-proportion z confidence interval), 13-20 1.PropZTest (one-proportion z test), 13-14 2.PropZInt (two-proportion z confidence interval), 13-21 2.PropZTest (two-proportion z test), 13-15 2.SampTest (two-sample .Test), 13-23 2.SampTInt (two-sample t confidence interval), 13-19 2.SampTTest (two-sample t test), 13-13 2.SampZInt (two-sample z confidence interval), 13-18 2.SampZTest (two-sample z test), 13-12 TInterval (one-sample t confidence interval), 13-17 T.Test (one-sample t test), 13-11 ZInterval (one-sample z confidence interval), 13-16 Z.Test (one-sample z test), 13-10 Stats input option, 13-6, 13-7 STAT TESTS menu, 13-9 statistical distribution functions. See distribution functions . S (continued) . statistical plotting, 12-31 Boxplot (regular box plot), 12-33 defining, 12-34 from a program, 12-37 Histogram, 12-32 ModBoxplot (modified box plot), 12-32 NormProbPlot (normal probability plot), 12-33 Scatter, 12-31 tracing, 12-36 turning on/off stat plots, 3-7, 12-35 viewing window, 12-36 xyLine, 12-31 statistical variables table, 12-29 stdDev( (standard deviation), 11-18, A-28 Stop, 16-15, A-28 Store (!), 1-14, A-28 StoreGDB, 8-19, A-28 StorePic, 8-17, A-29 storing graph databases (GDBs), 8-19 graph pictures, 8-17 variable values, 1-14 String4Equ( (string-to-equation conversions), 15-8, A-29 strings, 15-3 to 15-9 concatenation (+), 15-6, A-38 converting, 15-7, 15-8 defined, 15-3 displaying contents, 15-5 entering, 15-3 functions in CATALOG, 15-6 indicator ("), 15-3 length (length(), 15-8, A-13 storing, 15-5 variables, 15-4 student-t distribution probability (tcdf(), 13-31, A-29 probability density function (tpdf(), 13-30, A-30 sub( (substring), 15-9, A-29 subroutines, 16-15, 16-22 subtraction (N), 2-3, A-38 sum( (summation), 11-18, A-29 system variables, A-49 Index-13 .T. TABLE SETUP screen, 7-3 . T (continued) . time value of money (continued) variable (number of payment periods), 14-14 PMT variable (payment amount), 14-14 PV variable (present value), 14-14 P/Y variable (number of payment periods per year), 14-14 tvm_FV (future value), 14-7, A-31 tvm_I% (interest rate), 14-7, A-31 tvm_ (# payment periods), 14-7, A-31 tvm_Pmt (payment amount), 14-6, A-31 tvm_PV (present value), 14-7, A-31 TVM Solver, 14-4 variables, 14-14 TInterval (one-sample t confidence interval), 13-17, A-30 tpdf( (student-t distribution probability density function), 13-30, A-30 TRACE tables, 7-1 to 7-6 description, 7-5 variables, 7-3 to 7-5 tan( (tangent), 2-3, A-29 tanM1( (arctangent), 2-3, A-29 tangent (tan(), 2-3, A-29 Tangent( (draw line), 8-8, A-29 tangent lines, drawing, 8-8 tanh( (hyperbolic tangent), 15-10, A-29 tanhM1( (hyperbolic arctangent), 15-10, A-29 @Tbl (table step variable), 7-3 TblStart (table start variable), 7-3 tcdf( (student-t distribution probability), 13-31, A-29 technical support, B-12 TEST (relational menu), 2-25 TEST LOGIC (Boolean menu), 2-26 Text( instruction, 8-12, 9-6, A-29 placing on a graph, 8-12 Then, 16-9, A-11 thick () graph style, 3-9 TI.82 link differences, 19-9 transmitting to/from, 19-4, 19-8, 19-9 TI.83 features, 17, 18 keyboard, 2, 3 key code diagram, 16-20 Link. See linking menu map, A-39 TI.GRAPH LINK, 19-3 Time axes format, 6-8, A-30 time value of money (TVM) calculating, 14-6 C/Y variable (number of compounding periods per year), 14-14 formulas, A-54 FV variable (future value), 14-14 variable (annual interest rate), 14-14 cursor, 3-18 entering numbers during, 3-19, 4-8, 5-6, 6-9 expression display, 3-14, 3-18 Trace instruction in a program, 3-19, A-30 transmitting error conditions, 19-6 from a TI.82 to a TI.83, 19-9 items to another unit, 19-6 lists to a TI.82, 19-4, 19-8 stopping, 19-6 to an additional TI.83, 19-7 T (transpose matrix), 10-12, A-34 transpose matrix (T), 10-12, A-34 trigonometric functions, 2-3 T.Test (one-sample t test), 13-11, A-30 Index-14 . T (continued) . turning on and off axes, 3-14 calculator, 1-2 coordinates, 3-14 expressions, 3-14 functions, 3-7 grid, 3-14 labels, 3-14 pixels, 8-16 points, 8-14 stat plots, 3-7, 12-35 tvm_FV (future value), 14-7, A-31 tvm_I% (interest rate), 14-7, A-31 tvm_ (# payment periods), 14-7, A-31 tvm_Pmt (payment amount), 14-6, A-31 tvm_PV (present value), 14-7, A-31 two-proportion z confidence interval (2.PropZInt), 13-21, A-20 two-proportion z test (2.PropZTest), 13-15, A-20 two-sample -Test formula, A-52 two-sample t test formula, A-53 two-variable statistics (2.Var Stats), 12-25, A-31 . V (continued) . variables complex, 1-13 displaying and storing values, 1-14 equation solver, 2-10 graph databases, 1-13 graph pictures, 1-13 independent/dependent, 7-5 list, 1-13, 11-3 matrix, 1-13, 10-3 real, 1-13 recalling values, 1-15 solver editor, 2-9 statistical, 12-29 string, 15-4, 15-5 test and interval output, 13-28 types, 1-13 user and system, 1-13, A-49 VARS and Y.VARS menus, 1-21 variance( (variance of a list), 11-18, A-31 variance of a list (variance(), 11-18, A-31 VARS menu GDB, 1-21 Picture, 1-21 Statistics, 1-21 String, 1-21 Table, 1-21 Window, 1-21 Zoom, 1-21 Vertical (draw line), 8-6, A-31 viewing window, 3-11 vw/uvAxes (axes format), 6-8 .U. u sequence function, 6-3 user variables, A-49 uv/uvAxes (axes format), 6-8, A-31 uw/uwAxes (axes format), 6-8, A-31 .V. v sequence function, 6-3 1.Var Stats (one-variable statistics), .W. w sequence function, 6-3 12-25, A-31 2.Var Stats (two-variable statistics), warranty information, B-13 Web (axes format), 6-8, A-31 12-25, A-31 value operation on a graph, 3-25 web plots, sequence graphing, 6-11 While, 16-11, A-32 window variables function graphing, 3-11 parametric graphing, 4-5 polar graphing, 5-4 sequence graphing, 6-7 Index-15 .X. XFact zoom factor, 3-24 . Z (continued) . ZoomSto (store zoom window), 3-23, x-intercept of a root, 3-26 xor (Boolean) exclusive or operator, 2-26, A-32 x th root (x), 2-6 xyLine () plot type, 12-31 @X window variable, 3-12 A-33 ZPrevious (use previous window), 3-23, A-33 ZSquare (set square pixels), 3-21, A-33 ZStandard (use standard window), 3-22, A-33 Z.Test (one-sample z test), 13-10, A-34 ZTrig (trigonometric window), 3-22, .Y. YFact zoom factor, 3-24 Y= editor A-34 function graphing, 3-5 parametric graphing, 4-4 polar graphing, 5-3 sequence graphing, 6-4 Y.VARS menu Function, 1-21 Parametric, 1-21 Polar, 1-21 On/Off, 1-21 @Y window variable, 3-12 .Z. ZBox, 3-20, A-32 ZDecimal, 3-21, A-32 zero operation on a graph, 3-26 ZInteger, 3-22, A-32 ZInterval (one-sample z confidence interval), 13-16, A-32 zoom, 3-20 to 3-24 cursor, 3-20 factors, 3-24 function graphing, 3-20 parametric graphing, 4-8 polar graphing, 5-6 sequence graphing, 6-10 ZoomFit (zoom to fit function), 3-22, A-33 Zoom In (zoom in), 3-21, A-32 ZOOM menu, 3-20 ZOOM MEMORY menu, 3-23 Zoom Out (zoom out), 3-21, A-32 ZoomRcl (recall stored window), 3-23, A-33 ZoomStat (statistics zoom), 3-22, A-33 Index-16 ...
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