MATH 1112 FINAL EXAM REVIEW e. None of these. d. 1 e. None of these. d. 1 e. None of these. e. None of these. e. None of these.

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1 I. State the equation of the unit circle. MATH 111 FINAL EXAM REVIEW x y y = 1 x+ y = 1 x = 1 x + y = 1 II. III. If 1 tan x =, find sin x for x in Quadrant IV Give the exact value of each expression sin 1 0 Undefined. cos Undefined 1. sin10. cos

2 . cos 6. cos Undefined 7. tan 1 8. cot Undefined 9. sec csc0 Undefined 0 1 IV. Which of the following is a sketch of the graph of the given function on [0, )? 1. y = sin x

3 . y = cos x. y = tan x

4 . y = cot x. y = sec x

5 6. y = csc x

6 V. Simplify each expression. 1. cos( θ ) cosθ cosθ sinθ sinθ. sin( θ ) cosθ cosθ sinθ sinθ. tan( θ ) tanθ tanθ cotθ cotθ. sec( θ ) secθ secθ cscθ cscθ VI. Evaluate each expression. 1. arccos 7. 1 sin

7 . 1 csccot 1. tan ( 1) 7 6 VII. Which of the following is a sketch of one cycle of the graph of each function? 1. y = sin x. y ( x ) = cos + +

8 . y = tan x

9 . y = cot ( x+ ). y = sec x

10 6. y = csc( x ) 1

11 VIII. Use the sum or difference identities to evaluate each expression. 1. cos sin e. None of these. tan IX. Let α be in Quadrant I, β in Quadrant III, 7 cosα =, and tan β = ( α β) cos =? ( α β) sin + =? 0. ( α β) tan + =?

12 6 X. Change each sum or difference to a product. 1. sin 68 + sin cos0 cos18 sin 0 sin18 cos0 sin18 sin 0 cos18. sin x sin x cos xsin x sin x cos8x sin x cos xsin x. cos1x+ cos x cos17x 17x 7x sin sin 17x 7x sin cos 17x 7x cos cos. cos 0 cos 0 sin10 sin10 cos 0 cos10 XI. Let θ be in Quadrant II with 1 secθ =. 1. sin θ =? e. None of these 1

13 . cos θ =? 1. tan θ =? XII. Evaluate each of the following expressions using the half-angle identities. 1. sin cos tan XIII. If the terminal side of θ passes through the point (-,), find sin θ XIV. Solve each equation for 0 x <. 1. cos x= 1 sin x 1 1

14 7 11 0,,, 0,,, 0,,, , sin xcos x=,,,,. cos sin 1 0 x+ x =,, 6 6,, 6 6,, 7 11,, 6 6. cot x 1 = ,,,,,,, ,,, ,,, ,,,,,,, XV. Solve ABC for the missing part. 1. A= 90, a = 9, b= 1, B=? a =, b= 8, c= 10, C =?

15 . A= 0, b= 6, B= 0, c=? XVI. Give the radian measure of an angle that subtends an arc of length in a circle of radius None of these. XVII. Convert to degrees XVIII. Convert 60 to radians XIX. Simplify each expression. 1. sinθsecθ cotθ 1 sin θ tanθ. cos θ tan θ + cos θ 1 cot θ cos θ tan θ sin θ e. None of these. cscθ + secθ sinθ + cosθ 1 sinθ + cosθ csc θ + sec θ cscθsecθ

16 . ( ) sin x+ cos x sin x 1 1+ sin x sin xcos x. sec sec x tan x+ tan x x tan x 1 sec x tan x sin θ cotθ cos θsinθ cotθ secθ cosθsinθ cotθ XX. Change the product to a sum. 1. 6sin1 sin + +. sin xcos x cosx+ cos x sin x+ sin x cosx cos x cos x+ cos x. cos 8 sin 0 sin 68 sin1 1 1 sin 68 sin1 1 1 sin 68 + sin1 cos 68 + cos1

17 . cos 7xcosx 1 1 cos1x+ cos x 1 1 sin1x+ sin x 1 1 cos1x cos x 1 1 sin1x sin x XXI. Let the point 1, be a point on the terminal side of an angle θ in standard position. Find the sine and cosine of θ. 1 cos θ = ;sinθ = 1 sin θ = ;cosθ = 1 cos θ = ;sinθ = cosθ = ;sin θ = 1 1 XXII. For each of the following, give the quadrant in which the terminal ray of θ lies. 1. tanθ < 0 and cosθ > 0 I II III IV. cscθ > 0 and cot θ<0 I II III IV XXIII. Give the reference angle for the indicated angle

18 XXIV.Find the quadrant in which the indicated angle lies I II III IV I II III IV.. I II III IV. 1 I II III IV

19 XXV. Which of the following angles are coterminal with the given angle? XXVI.Give the amplitude of the function f ( x) = 7 cos x XXVII.Give the period of the function f ( x) = 8sin 9 x XXVIII.Give the period of the function f ( x) = tan x XXIX.Given the following data set for ABC, how many triangles can be drawn?

20 1. a = 1, b= 0, A= 1 0. a = 8, b= 1, A= 1 0 XXX. If cosθ =, θ in Quadrant III, find the value of tanθ XXXI. The length of an arc of the unit circle is as given. Name the quadrant within which the terminal point would lie. 1. t = I II III IV.. 1 t = 1 I II III IV.. t = 0 9 I II III IV.

21 . t =.78 I II III IV. XXXII.Give the terminal point on the unit circle for an arc of the length below. 1. t = 7 6 1, 1, 1, 1, None of these.. t =,,, ( 0, 1) None of these.. t = 1, 1, 1, 1, XXXIV.Complete the following statements: 1. 1 sin θ = tan θ sinθ cosθ

22 cos θ. sec θ tan θ = secθ tanθ sinθ 1 cos θ. = cos 7x sin 7 x 1 sin1x cos1x 0. 1 cos 0 = cos sin sin100 cos cot 9 x = csc 9x cot 10x sec 9x cos 9x 6. cos ( θ ) + = cosθ sinθ sinθ cosθ 7. ( θ ) sin + = cosθ sinθ sinθ cosθ

23 ANSWERS: I. c II. d III. 1. d. a. c. c. a 6. a 7. b 8. d 9. d 10. a IV. 1. b. a. a. b. b 6. a V. 1. b. d. a. b VI. 1. d. c. d. b VII. 1. d. c. c. a. a 6. a VIII. 1. d. c. a IX. 1. b. c. d X. 1. d. d. d. a XI. 1.. d. a XII. 1. b. c. c XIII. b XIV. 1. a. d. c. a XV. 1. b. b. a XVI. b XVII. a XVIII. b XIX. 1. d. a. d. c. d 6. c XX. 1. a. b XXI. a XXII. d XXIII. 1. c. d. a XXIV.1. b. a. d. b XXV. 1. b. a XXVI. b XXVII. d XXVIII. b XXIX. 1. b. d

Math 104 Final Exam Review

Math 104 Final Exam Review Math 04 Final Exam Review. Find all six trigonometric functions of θ if (, 7) is on the terminal side of θ.. Find cosθ and sinθ if the terminal side of θ lies along the line y = x in quadrant IV.. Find