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### L09_blanks

Course: MAC 1114, Spring 2011
School: University of Florida
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Word Count: 630

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10 Lecture Day 09 for 2/08/2011 Generalizing Trigonometry, part Tres is 0 Slide: 2 of 16 More Generalizations If a point (x,y) in the plane is on the unit circle then that points coordinates give the values of the trigonometric functions for any angle whose terminal side goes through that point. But what if the point is not on the unit circle? In that case, we can normalize the point by dividing its...

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10 Lecture Day 09 for 2/08/2011 Generalizing Trigonometry, part Tres is 0 Slide: 2 of 16 More Generalizations If a point (x,y) in the plane is on the unit circle then that points coordinates give the values of the trigonometric functions for any angle whose terminal side goes through that point. But what if the point is not on the unit circle? In that case, we can normalize the point by dividing its ______________ by the points norm, r, its _______________ from the origin. 1 is 0 Slide: 3 of 16 Trig. Functions defined by Normalized Pts. Let (x, y) be a point in space. Let r = Then, Notice: 1) From the last slide we know ___________ is a point on the unit circle. 2) This definition of the 6 trig. functions agrees with the unit circle definition when r = ___ 3) And agrees with the right triangle definition if the point (x, y) is in quadrant ___. 4) If x = 0, secant and tangent are _____________. 5) If y = 0, cosecant and cotangent are _____________. Slide: 4 of 16 is 0 Evaluating the Trig functions for Any Point The point lies on the terminal ray of the angle standard position. in Find the six trigonometric function using the normalized point Definition. What is the Normalized Point? 2 is 0 Slide: 5 of 16 Examples 1) Let point (-5, -12) on the terminal side of the angle . Find the sine, cosine, and tangent values of the angle . is 0 Slide: 6 of 16 Examples 2) If and lies in Quadrant IV, find the secant, cosecant, and cotangent trigonometric function values. 3 is 0 Slide: 7 of 16 Reference Angles & Triangles Let be an angle in standard position. The reference angle to is the acute angle formed by the terminal side of and the x-axis. The reference triangle to is the triangle whose hypotenuse ___________ the terminal ray of and whose base ___________ the x-axis. Some individuals prefer to label the base length and height as _________________ when the leg of the triangle matches up with a negative axis. The hypotenuse is always ____________. is 8 0 Slide: of 16 Reference Angle & Triangle Cases The following four cases are all that are possible: 4 is 0 Slide: 9 of 16 Trig function Values The values of the Trig. Functions evaluated at the angle , are ________ times the values of Trig. Function evaluated using the reference angle or using right triangle trigonometry on the reference triangle. The following table describes all cases. To evaluate the trig function of an arbitrary angle, locate the angle in the plane and identify the reference angle. Then either 1) use one of the formula in the table above or 2) 2) draw a reference triangle and account for positive and negative. is 0 Slide: 10 of 16 Examples Find the reference angle for 1) 2) 5 is 0 Slide: 11 of 16 More Examples Use reference angles or reference triangles to find 1) 2) is 0 Slide: 12 of 16 Even More Examples Use reference angles or reference triangles to find 3) 4) 6 is 0 Slide: 13 of 16 The Examples Just Keep Coming 1) Given 2) If and and , find is in Quadrant III, find . . is 0 Slide: 14 of 16 Word Problem Examples Ex. A giant redwood tree casts a shadow 600 feet long. Find the height of the tree if the angle of elevation of the sun is 30 degrees. 7 is 0 Slide: 15 of 16 Another Word Problem Example Ex. From a point on the ground 500 feet from the base of a building, an observer find the angle of elevation to the top of the building is 30 degrees and that the angle of elevation to the top of a flagpole atop the building is 32 degrees. Find the height of the building and the length of the flagpole. is 0 Slide: 16 of 16 So what the heck do I have to memorize Memorize the cardinal (the book calls them quadrant) angles and the special triangle angles in QI, (in Maroon) The special angles in QI are the reference angles to those in QII, QIII, and QIV (in Dark Blue). Symmetry can used to find all remaining terminal points. (Maroon for Memorize, Dark Blue for Derive) 8
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University of Florida - MAC - 1114
Day 11Lecture 10for 2/10/2011Graphing Sine and Cosineis 0Slide: 2 of 10Intro.Weve just spend a lot of time talking about the different ways ofdefining the 6 trigonometric functions and a bit about thedifferent case that come up when you evaluate
University of Florida - MAC - 1114
Day 12Lecture 11for 2/15/2011Graphing Sine and Cosine,with V/H SCRis 0Slide: 2 of 14Vertical S.C.R.Suppose t is fixed and we have two functions f(x) and v(x), whereThen (t, _ ) is a point on the graph of f , and(t, _ ) is a point on the graph of
University of Florida - MAC - 1114
Day 14Lecture 12for 2/22/2011Graphing Sine and Cosine,with V/H SCR andTranslationsis 0Slide: 2 of ?Last Time in MAC1114We examined the differences betweenand.1) The _ by a on the outside, causes the originaly-coordinates to become _ by a.2)
University of Florida - MAC - 1114
Day 15Lecture 13for 2/24/2011Graphing other Trig.Functionsis 0Slide: 2 of 14Recap!All transformed trig functions have a form analogous to:Remember, you can find all the key information before you ever startgraphing, like Min. y-coordinates:Sta
University of Florida - MAC - 1114
Day 16Lecture 13 part 2 &amp; 14for 3/01/2011Graphs of Tan, Cot&amp; Inverse Functionsis 0Slide: 2 of 14Basic TangentSince Tangent has period _, its basic one cycle is different thansine, cosine, secant, and cosecant.1is 0Slide: 3 of 14Basic Cotangen
University of Florida - MAC - 1114
Day 17Lecture 14for 3/03/2011Inverse Functionsis 0Slide: 2 of 14L14: Precalc. Review 1Points on a graph are like a stepping stone from the x-axis to the yaxis, pictorially .Examples:As long as we can hop from an x-coordinate to just _ y-coordinat
University of Florida - MAC - 1114
Day 18Lecture 15for 3/03/2011Problems involvingInverse Functionsis 0Slide: 2 of 12L14: From Last TimeYou should know the inverse ofSine, Cosine, Tangent &amp; Cotangent.We are not covering the inverse ofcosecant or secant. And you knowif Mr. M isn
University of Florida - MAC - 1114
Day 18Lecture 15for 3/03/2011Problems involvingInverse Functionsis 0Slide: 2 of 12L15: Review/RecapCase 3:Case 3.5:1is 0Slide: 3 of 12L15: Review/RecapCase 5:Case 6:is 0Slide: 4 of 12L16: Ready? Word Problems!To solve a right triangle m
University of Florida - MAC - 1114
Day 19Lecture 17for 3/22/2011Word Problems involvingInverse Functionsis 0Slide: 2 of 12L16 Review: The Flag Pole ProblemEx: A woman standing on a hill sees a flagpole that she knows is 60 fttall. The angle of depression to the bottom of the pole
University of Florida - MAC - 1114
Day 21Lecture 18for 3/24/2011Mostly About Identitiesis 0Slide: 2 of 10L17 Alternate Way to Graph TangentYou may or may not have had trouble. Here is an alternative Ivebeen showing students whove see me in Office Hours.The book ( and myself) say 1
University of Florida - MAC - 1114
Day 22Lecture 19for 3/29/2011Mostly About Identitiesis 0Slide: 2 of 10L18 Dont Forget the BasicsAn equation is an Identity if it is true for _ or _ values ofits variables.3. Pythagorean Identities:4. Even/Odd Identities:5. Cofunction Identities
University of Florida - MAC - 1114
Day 23Lecture 20for 3/31/2011Verifications &amp; Equationsis 0Slide: 2 of 12L19 Dont Forget the Basics3. Pythagorean Identities:Cross Over from MAC1140:Combos ARE COOL:1is 0Slide: 3 of 12L19 Its really More of a Guideline1) Start with one Side.
University of Florida - MAC - 1114
Day 25Lecture 21for 4/07/2011Equationsis 0Slide: 2 of 12L19 Dont Forget the Basics3. Pythagorean Identities:L20 STEPS for Simple(r) Trig. Equations1) First, Isolate the trig. function.2) Solve for the angles in just one cycle.3) Add K times the
University of Florida - MAC - 1114
MahoneyL21 Suggested ExercisesMAC1114 Spring 2011 UFName: _ Per: 2 3 7 UF ID: _ _ _ _ _ _ _ _Suggested Exercises for L21: pages 394 - 397 #1 -4, 7, 8, 11, 12, 14, 21, 22, 25, 28, 33-43 odd, 45, 47(show algebra), 60, 61, 63, 67, 70, also do following
University of Florida - MAC - 1114
Day 26Lecture 22for 4/12/2011E.Q.s + Sum &amp; Diff. Identitiesis 0Slide: 2 of 12L19 Dont Forget the Basics3. Pythagorean Identities:L20 STEPS for Simple(r) Trig. Equations1) First, Isolate the trig. function.2) Solve for the angles in just one cycl
University of Florida - MAC - 1114
Day 27Lecture 23for 4/14/2011Last (day) of the Identitiesis 0Slide: 2 of 13L22 Sum and Difference Recap!Memorize and or learn how to derive. The arrows indicate the orderyou can derive them.1is 0Slide: 3 of 13L22 Old Problems, New Details.Ex:
University of Florida - MAC - 1114
Day 27Lecture 23for 4/14/2011Last (day) of the Identitiesis 0Slide: 2 of 13L22 Sum and Difference Recap!Memorize and or learn how to derive. The arrows indicate the orderyou can derive them.1is 0Slide: 3 of 13L22 Old Problems, New Details.Ex:
University of Florida - MAC - 1114
First:BobE.Last Moticon:UFID#:Nick:TheStickManHometowMr.MsMindn:EmailBob.E.Moticon@gmail.net:MajorYearFineArts:CareerJunior:ActionMoviesAspirations:SomethingIhaveaccomplished,workedhardfor,and/orareproudof:SurvivingMr.MahoneysGraph
University of Florida - MAC - 1114
MAC 1114SectionMeeting TimeRoomFinal Exam2691TR2, 8:30 9:20 a.m. in LIT 219 Tue. 04/26 12:30 PM3018 TR3, 9:35 10:25 a.m. in LIT 201 Fri. 04/29 12:30 PM3474TR2, 1:55 2:45 p.m. in LIT 127 Fri. 04/29 10:00 AMInstructor: Matt MahoneyOffice: 467 Lit
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Chapter 06 - Interest Rates And Bond ValuationCHAPTER 6INTEREST RATES AND BONDVALUATIONAnswers to Concepts Review and Critical Thinking Questions1.No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasurys
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Chapter 07 - Equity Markets and Stock ValuationCHAPTER 7EQUITY MARKETS AND STOCKVALUATIONAnswers to Concepts Review and Critical Thinking Questions1.The value of any investment depends on its cash flows; i.e., what investors will actually receive. T
University of Texas - FIN 320F - 320F
Chapter 10 - Some Lessons From Capital Market HistoryCHAPTER 10SOME LESSONS FROM CAPITALMARKET HISTORYAnswers to Concepts Review and Critical Thinking Questions1.They all wish they had! Since they didnt, it must have been the case that the stellar p
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11-1McGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rightsWhy Study Finance?l Marketingl Budgets,marketing research, marketing financial productsl Accountingl Dualaccounting and finance function, preparation offinancial st
University of Texas - FIN 320F - 320F
McGraw-Hill/Irwin4-1Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Key Concepts and SkillsBeable to compute the future value of aninvestment made todayBe able to compute the present value of cash tobe received at some future
University of Texas - FIN 320F - 320F
McGraw-Hill/Irwin5-1Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Key Concepts and SkillsBeable to compute the present value ofmultiple cash flowsBe able to compute loan paymentsBe able to find the interest rate on a loanU
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McGraw-Hill/Irwin6-1Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Basic ValuationValue of asset = PV of expectedfuture CFsBasic ValuationCFCFCFAsset12N=V=++12Nvalue(1 + r ) (1 + r )(1 + r )CFt = the cash flow
University of Texas - FIN 320F - 320F
7-1McGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Key Concepts and SkillsUnderstandhow stock prices depend on futuredividends and dividend growthBe able to compute stock prices using thedividend growth model
University of Texas - FIN 320F - 320F
McGraw-Hill/Irwin10-1Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Key Concepts and SkillsKnowhow to calculate the return on aninvestmentUnderstand the historical returns on varioustypes of investmentsUnderstand the histor
University of Texas - FIN 320F - 320F
McGraw-Hill/Irwin11-1Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Key Concepts and SkillsKnowhow to calculate expected returnsUnderstand the impact of diversificationUnderstand the systematic risk principleUnderstand the s
University of Texas - FIN 320F - 320F
Name_Fin 320F Mid-term Exam Summer 20111. The primary goal of financial management is to a. Maximize net incomeb. Maximize stock pricec. Minimize costsd. Maximize firm sizee. Maximize agency costs2.Which of the following is false? A corporation:
University of Texas - FIN 320F - 320F
Exam2 FIN370-01 Winter 2011 Key1. If shareholders are granted a preemptive right they will be:A. given the choice of receiving dividends in cash or in additional shares of stock.B. granted shares that receive additional voting privileges.C. given the
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Exam2 FIN370 Fall 2008 KeyVersion B1. A call provision in a bond agreement grants the issuer the right to:A. repurchase the bonds prior to maturity at a pre-specified price.B. change the coupon rate provided the bondholders are notified in advance.C.
University of Texas - FIN 320F - 320F
Assignment Print View1 of 101.http:/ezto.mhhm.mcgraw-hill.com/hm_finance.tpxaward:5 pointsAssume the total cost of a college education will be \$390,000 when your child enters college in 18 years.You presently have \$64,000 to invest.Required:What
University of Texas - FIN 320F - 320F
Assignment Print View1 of 111.http:/ezto.mhhm.mcgraw-hill.com/hm_finance.tpxaward:4 pointsWhich one of the following represents additional compensation provided to bondholders to offset the possibility that the bondissuer might not pay the interest
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EDUCATIONFORUMSCIENCE EDUCATIONDefeating Creationism in theCourtroom, But Not in the ClassroomSixty percent of U.S. high school biology teachersare not advocates for either evolutionary biologyor nonscientic alternatives.Just over 5 years ago, the
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University of Texas - EDP - 310
Group Created Exam 2 QuestionsGroup 11.)Bobby is studying for his test and having trouble to find out how he wants to accomplish some ofthe reading activities required and retain some of the material. He decides that hes going to usehis own personal
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QuickTime and aTIFF (Uncompressed) decompressorare needed to see this picture.
University of Texas - EDP - 310
InformationProcessingStrategiesComparativeOrganizerofStrategiesfromAllCategoriesStrategyNameCategoryType ofMemoryDescriptionExample(if possible)Which of my classes will Iuse this strategy or howFirst-LetterMethodRehearsalShortTermUsing fi
University of Texas - EDP - 310
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University of Texas - EDP - 310
Your Name: _Instructor Name: _EID: _Time Class Meets: _EDP ALTERNATE RESEARCH ASSIGNMENTThe following assignment is REQUIRED for all EDP students who did not fully participate in theEducational Psychology subject pool research studies. To pass and r
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University of Texas - EDP - 310
Sun Hudson CaseThis case involves the patient, Sun Hudson, a baby born with a skeletal malformationcalled thanatophoric dysplasia. This disorder causes extreme dwarfism and usually bringsdeath within a few months or years. Suns mother, Wanda Hudson, re
University of Texas - EDP - 310
EDP 3101Unit 1 Learning Objectives for Course ContentTopic: Model of Strategic Learning1. List and discuss the four components of the Model of Strategic Learning, and give examples ofeach. Explain how each of these components can contribute to academ
University of Texas - EDP - 310
EDP 3101Unit 2 Learning ObjectivesTopic: Academic Environment (AE)1. Discuss how developing awareness of the academic environment can contribute to becoming a morestrategic learner.2. List and describe the 4 parts of the academic environment (from t
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1A Twist of WaterBy Caitlin Montanye ParrishCo-created with Erica L. WeissCHARACTERSNOAH 39, white, a teacherJIRA 17, black, his daughterLIAM 26, white, a teacherTIA 33, black, JIRA's birth mother2Act OneScene 1: Lost[NOAH stands alone. There
University of Texas - TD - 301
598 /Forum on Black Theatreblack actors playing a wide repertoire from Langston Hughess Mulatto to NtozakeShanges for colored girls . . . ; from Sissle and Blakes The Chocolate Dandies to AugustWilsons Gem of the Ocean.If the reader wishes to dene pl
University of Texas - TD - 301
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University of Texas - TD - 301
University of Texas - TD - 301
Excerpted from Robert Brustein, Subsidized SeparatismThe foundation of this long tirade is Wilson's insistence on black culture,particularly black theatre, not only as an unparallelled achievement butalso a singular and discrete experience of life. It
University of Texas - TD - 301
Excerpted from August Wilson, The Ground on Which We StandTheatre is part of art history in terms of its craft and dramaturgy, but it is part ofsocial history in terms of how it is financed and governed. By making moneyavailable to theatres willing to
University of Texas - TD - 301
&quot;Trifles&quot; by Susan Glaspell (1916)Scene: The kitchen in the now abandoned farmhouse of John Wright, a gloomykitchen, and left without having been put in order-unwashed pans under thesink, a loaf of bread outside the breadbox, a dish towel on the table-
University of Texas - TD - 301
Truth is not an individual perception. There are 66 LORT theatres strung likepearls across this country from Maine to Alaska. Only one of them is dedicated topreserving and promoting black culture. This gives us a theatre not only skewedtoward whites a
University of Texas - UGS - 302
University of Texas - UGS - 302
University of Texas - UGS - 302
University of Texas - UGS - 302
University of Texas - UGS - 302