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### Test2Trig

Course: MAC 1114, Spring 2009
School: University of Florida
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Word Count: 366

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A MAC Name: Version 1114 Test 2 10/23/2007 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5 points] I. MULTIPLE CHOICE 1. For y = 3 tan(2x + ), suppose A=amplitude, T =Period and 2 = phase shift. Then which of the following holds. a) A=3 T = A = 3 b) 2 2 = 2 2. The exact value of cos1 ( 6 A=3 b) 6 d) 2 = 4 T= = 4 a) c) T= A=3 T= A = 3 e) 2 T = =...

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A MAC Name: Version 1114 Test 2 10/23/2007 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5 points] I. MULTIPLE CHOICE 1. For y = 3 tan(2x + ), suppose A=amplitude, T =Period and 2 = phase shift. Then which of the following holds. a) A=3 T = A = 3 b) 2 2 = 2 2. The exact value of cos1 ( 6 A=3 b) 6 d) 2 = 4 T= = 4 a) c) T= A=3 T= A = 3 e) 2 T = = 4 = 2 3 2) c) is 7 6 d) 5 6 e) 2 3 3. Suppose = tan1 3 . Choose the appropriate diagram corresponding to the angle in standard position. 2 4. tan(tan1 x) = tan1 (tan x) for all x in the Real numbers True False 5. sin(sin1 ) = True False 6. sin True False = cos 2 [1 pt extra credit] In problem 4, explain why. [19 points] II. FREE RESPONSE [6 pts] 1. Suppose we have y = A sec( (x T= 2 )), where A = 2, = 2 , = 1 and hence the period 2 = 1. Sketch the graph of the function y with this characteristics. *Recall you may rst nd the corresponding cosine graph. 2 [3 pts] 2. Find the exact value of sec sin1 5 [6 pts] 3. Establish the identity csc cot = sin 1 + cos [4 pts] 4.- Find the exact value of the following (in part a) choose ONLY one problem) a) sin 11 6 b) cos 22.5 or cos 315 Name: Version 1114 B MAC Test 2 10/23/2007 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5 points] I. MULTIPLE CHOICE 1. For y = 3 tan(2x + ), suppose A=amplitude, T =Period and 2 = phase shift. Then which of the following holds. a) A=3 b) 2 = 4 A = 3 T = T= 2. The exact value of cos1 ( 6 A=3 2 = 2 T= a) c) b) 5 6 d) 2 A=3 T= = 4 A = 3 e) 2 T = = 4 = 2 3 2) c) is 7 6 d) 6 e) 2 3 3. Suppose = tan1 2 . Choose the appropriate diagram corresponding to the angle in standard position. 3 4. tan(tan1 x) = tan1 (tan x) for all x in the Real numbers True False 5. sin1 (sin ) = 2 True False 6. sin True False 2 = cos 2 [1 pt extra credit] In problem 4, explain why. [19 points] II. FREE RESPONSE [6 pts] 1. Suppose we have y = A sec( (x T= 2 )), where A = 2, = 2 , = 1 and hence the period 2 = 1. Sketch the graph of the function y with this characteristics. *Recall you may rst nd the corresponding cosine graph. 2 [3 pts] 2. Find the exact value of sec sin1 5 [6 pts] 3. Establish the identity csc cot = sin 1 + cos [4 pts] 4.- Find the exact value of the following (in part a) choose ONLY one problem) a) sin 11 6 b) cos 22.5 or cos 315
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University of Florida - MAC - 1114
Name: MAC 1114 Test 2 PART I10/22/2009 [6pt] 1. Sketch the graph of 3 csc( x + ). Remember to label, Amplitude, Period, Phase Shift and 3 3 Asymptotes![2pt] 2. Answer TRUE OR FALSE a. b. c. The range of sin1 x is [ , ] 22 cos1 (cos( ) = 2 2 sin(sin1 3
University of Florida - MAC - 1114
Name:MAC 1114 Test 311/29/2007SHOW ALL YOUR WORK. Answers without procedure will be graded zero.[5 pts] 1. Solve the following equation, nding the exact value of in radians, express as fractions of on the interval 0 &lt; 2 .3 tan2 = 12. Solve each equ
University of Florida - MAC - 1114
Name:Version AMAC 1114 Test 203/06/2008[5 points] I. MULTIPLE CHOICE1. For y = 5 sin(2x + ), suppose AM =amplitude, T =Period and2=phase shift. Then which of thefollowing holds.a)AM = 5b)AM = 5c)AM = 5d)AM = 5e)AM = 5T = T =T =T =T
University of Florida - MATH - MAC1147
MAC 1147 (3067) - Quiz #1Name:For full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)112+6232Simplify the radical expression below. (2 points)8a5b23
University of Florida - MATH - MAC1147
MAC 1147 (3067) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)112+62311213413+421+=+===.6236666632Simplify t
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)412+5 3 15412125212 5 + 293+=+===.5 3 1515 15 1
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #1Name:For full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)132+2 10 52Simplify the radical expression below. (2 points)27x7
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)132+2 10 513253453+463+=+===.2 10 510 10 101
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #2Name:For full credit, you must show all work and circle your nal answer.1Write the rational expression in simplest form.Hint: Dont forget to specify domain restrictions, if any. (1 point)9x2 + 9 x2x + 22Find all solutions
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #2Name:KeyFor full credit, you must show all work and circle your nal answer.1Write the rational expression in simplest form.Hint: Dont forget to specify domain restrictions, if any. (1 point)9x2 + 9 x2x + 29x2 + 9 x9x(x +
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #3Name:KeyFor full credit, you must show all work and circle your nal answer.1Rewrite the expression using negative exponents. (1 point)2x2(x + 1) 32x(x + 1)2= (2 x)(x + 1)2/3 .Identify all x or y intercepts and graph t
University of Florida - MATH - MAC1147
MAC 1147 (3067) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(2x3 + 14x2 20x + 7) (x + 6)Make sure to write your answer out after performing the long
University of Florida - MATH - MAC1147
MAC 1147 (3067) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)2x2x+6(2x3 + 14x2 20x + 7) (x + 6)+ 2x 322x3 + 14x2 20x 2x3 12x2+72x2 20x 2x2
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(3x3 16x2 72) (x 6)Make sure to write your answer out after performing the long division
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(3x3 16x2 72) (x 6)3x2 + 2x + 12x63x3 16x2 3x3 + 18x2 722x2 2x2 + 12x312x 72
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(9x3 16x 18x2 + 32) (x 2)Make sure to write your answer out after performing the long di
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(9x3 16x 18x2 + 32) (x 2)9x2x2 169x3 18x2 16x + 32 9x3 + 18x29 16x + 3216x 32
University of Florida - MATH - MAC1147
MAC 1147 - Quiz #6 PracticeName:For full credit, you must show all work and circle your nal answer.1The interest rate for a bank account is 7.5%. Find the annual percentage yield if interest is compounded:(2 points)(a) Weekly(b) Continuously[Note:
University of Florida - MATH - MAC1147
MAC 1147 - Quiz #7 PracticeName:KeyFor full credit, you must show all work and circle your nal answer.1The interest rate for a bank account is 7.5%. Find the annual percentage yield if interest is compounded:(2 points)(a) Weekly(b) Continuously[N
University of Florida - MATH - MAC1147
MAC 1147 (3067) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.tan(t) = tan(t)tan(t) = tan(t)2csc(t) = csc(t)csc(t) = csc(t)1(2 poi
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.sec(t) = sec(t)sec(t) = sec(t)2csc(t) = csc(t)csc(t) = csc(t)tan(t) =
University of Florida - MATH - MAC1147
MAC 1147 (3069) - Quiz #8Name:KeyFor full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.sec(t) = sec(t)sec(t) = sec(t)csc(t) = csc(t)csc(t) = csc(t)sec(t)
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.cos(t) = cos(t)cos(t) = cos(t)2sin(t) = sin(t)sin(t) = sin(t)(2 point
University of Florida - MATH - MAC1147
MAC 1147 (4258) - Quiz #8Name:KeyFor full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.cos(t) = cos(t)cos(t) = cos(t)sin(t) = sin(t)sin(t) = sin(t)cos(t)
University of Florida - MATH - MAC1147
MAC 1147 LECTURE OUTLINEYou should read the textbook sections covered in each days lecture beforeclass. After each lecture, review your notes and the text to make sure youunderstand the main ideas to prior to working the exercises.If you have question
University of Florida - MATH - MAC1147
University of Florida - MATH - MAC1147
FinalExamReviewforMAC1147Spring2009PartI:2pointseach1. True/False:If231isapolynomialofdegree4.a. TRUEb. FALSE1when2. If isinverselyproportionalto and4,then2a. TRUEb. FALSE,3. |2112a.1|2_.1b.4. Howmanysolutionsdoestheequationtan 4
University of Florida - MATH - MAC1147
Final Exam Review KEY for MAC1147 Spring 20091.2.3.4.5.FALSEFALSEBAC6.7.8.9.10.DBBBC11.12.13.14.15.BADCB, Ooops. There is a typo, it should be a 5 in the denominator by .16.17.18.19.20.EABCC21.22.23.24.25.AB
University of Florida - MATH - MAC1147
MAC 1147 LECTURE OUTLINEYou should read the textbook sections covered in each days lecture beforeclass. After each lecture, review your notes and the text to make sure youunderstand the main ideas to prior to working the exercises.If you have question
University of Florida - MATH - MAC1147
Lecture 2: Section A.2Exponents and RadicalsInteger ExponentsDef. Ifthenis a real number andis a positive integer,=where is the base andis the exponent or power.ex. (3)4 = 34 =(2)3 = 23 =NOTE:1) Zero exponent: If= 0, then2) Negative expon
University of Florida - MATH - MAC1147
Lecture 5: Section A.5Solving EquationsDef. An equation in is a statement that twoalgebraic expressions are equal.To solve an equation is to nd all values ofwhich the equation is true.forSuch values of are solutions (or roots, zeros)of the equatio
University of Florida - MATH - MAC1147
Lecture 8, part I: Section 1.3Linear Equations in Two VariablesDef. The equation++ = 0 is the generalform of a linear equation in two variables.The slopeofis dened by the formula=( x2 , y 2 )( x1 , y 1 )Slope as a Rate of ChangeFor line ,is
University of Florida - MATH - MAC1147
Lecture 11: Section 1.8Combinations of FunctionsAlgebra of FunctionsLet and be two functions with domains. We dene some new functions:NameDenitionandDomainex. Given ( ) =function3and ( ) =and its domain.. Find theex. If ( ) =and ( ) =func
University of Florida - MATH - MAC1147
Lecture 12: Section 1.9Inverse FunctionsDef. If a function is a set of ordered pairs ( , ),then inverse relation of is the set of orderedpairs ( , ).ex. Find the inverse relation of the following functions. Is the inverse a function?1): cfw_(2, 2),
University of Florida - MATH - MAC1147
Lecture 15: Section 2.4Complex NumbersConsider the equation2= 1.Def. The imaginary unit, , is the number suchthat2= 1 or= 1Power of1=5=2= 13=4=61 ==7=8=Therefore, every integer power of can be written as, 1, , 1.In general, d
University of Florida - MATH - MAC1147
Lecture 16, Part I: Section 2.5Zeros of Polynomial FunctionsLinear Factorization TheoremEvery polynomial function ( ) of degree &gt; 0 canbe factored into linear factors (not necessarilydistinct) of the form( )=where1, 2, . . . ,(1 )(2) ()are co
University of Florida - MATH - MAC1147
Lecture 17: Section 2.6Rational FunctionsHoles and Vertical AsymptotesThe graph of a rational function ( ) =hole at=if()has a()1. both ( ) and ( ) have the common factor( ), and2. the simplied denominator DOES NOT havethe factor ( ).NOTE: To
University of Florida - MATH - MAC1147
Lecture 18: Section 2.7Nonlinear InequalitiesTo Solve a Polynomial Inequality1. Write the inequality with 0 on the right hand sideto obtain one of the following:( )&gt;0( )0( )&lt;0( )02. Find all real zeros of the polynomial ( ). Thesezeros are the c
University of Florida - MATH - MAC1147
Lecture 21: Section 3.2Logarithmic FunctionsRecall the graph of exponential function ( ) =&gt; 1:,(0,1)Since ( ) is one-to-one, it has an inverse function.Def. The logarithmic function with base ,where &gt; 0 and = 1 is written ( ) = log andis dened by
University of Florida - MATH - MAC1147
Lecture 23: Section 3.4Exponential and Logarithmic EquationsTwo basic strategies for solving exponential orlogarithmic equations:1. One-to-One Properties=logif and only if= logif and only if2. Inverse Propertieslog=log=ex. Solve for :1) 2
University of Florida - MATH - MAC1147
Lecture 24: Section 3.5Exponential and Logarithmic ModelsFour common types of mathematical models involving exponential functions and logarithmic functions:1. Exponential growth model:where== amount at time= amount at time 0= relative growth rate,
University of Florida - MATH - MAC1147
11211211212211111111111117212
University of Florida - MATH - MAC1147
Lecture 30: Section 4.7Inverse Trigonometric FunctionsThe Inverse Sine Function11Lets restrict the domain to the interval , .22Then = sin is one-to-one.Def. The inverse sine function is dened by= sin1if and only ifwith domain [1, 1] and range ,
University of Florida - MATH - MAC1147
MAC 2311LECTURE OUTLINE and HOMEWORK EXERCISESStewart: Calculus, Early Transcendentals, 6th editionYou should read the textbook sections covered in each dayslecture before class. After each lecture, review your notes andthe text section to make sure
University of Florida - MATH - MAC1147
Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi
University of Florida - MATH - MAC1147
Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi
University of Florida - MATH - MAC1147
Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi
University of Florida - MATH - MAC1147
Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi
University of Florida - MATH - MAC1147
MAC1147: Quiz #1 Solutions09/01/20091. LetAA = 0, , 0.67,12, 5, ,3(3)2.State which elements ofare(3)2 = 3)(a) whole numbers; (0,(b) integers; (0, -5,(3)2 = 3)10.67, -5, ,3(,2)(c) rational numbers; (0,(d) irrational numbers.(3)2 = 3)
University of Florida - MATH - MAC1147
MAC1147: Quiz #209/08/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #309/15/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #409/22/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #509/29/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1a
University of Florida - MATH - MAC1147
MAC1147: Quiz #610/06/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #710/20/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #810/27/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.
University of Florida - MATH - MAC1147
MAC1147: Quiz #911/3/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.1. F
University of Florida - MATH - MAC1147
MAC1147: Quiz #1011/17/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.y
University of Florida - MATH - MAC1147
MAC1147: Quiz #1112/1/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.1.
University of Florida - MATH - MAC1147
MAC 1147 Review 1, Spring 2011Exam 1 covers Lectures 1-81. Write without absolute value signs and simplify:2 + 2 1(b) 5 3 (a)+1(c) 312 4 + 1 if &gt; 300 3 15 12, , 0.9, 4, , 3 8, , , , , 161/4 , 0.08 .300 5 2List the elements that belong to each
University of Florida - MATH - MAC1147
MAC 1147 Review 2, Spring 2011Exam 2 covers Lectures 9-181. Classify the following functions as even, or odd, or neither even nor odd:12(b) ( ) = (a) ( ) =2+51(c) ( ) = 3 (d) ( ) = 2. Find the average rate of change ( ) =11on the interval [3