ACP PreCalculus Name__________________________________Final Exam Review Packet

Remember to change modes in your calculator and show all work.All graphing problems should be completed in radian mode.

Chapter 6

Convert the angle in degrees to radians. Express the answer as multiple of .

1) 105° 1)

Convert the angle in radians to degrees.

2) 910

2)

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Findthe exact value of the indicated trigonometric function of t.

3) (29

, 779

) Find tan t. 3)

4) (49

, -659

) Find csc t. 4)

A point on the terminal side of an angle is given. Find the exact value of the indicatedtrigonometric function of .

5) (4, -5) Find cot . 5)

Find the exact value of the expression.

6) sin3

- cos6

6)

7) csc 60° - cos 45° 7)

8) cos 203

8)

9) cos 120° tan 60° 9)

1

10) What is the domain of the sine function? 10)

11) For what numbers is f( ) = tan not defined? 11)

12) What is the range of the cosine function? 12)

13) Determine the sign of the trigonometric values listed below.(i) sin 250°(ii) tan 330°(iii) cos(-40°)

13)

Name the quadrant in which the angle lies.

14) cot > 0, sin < 0 14)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression.

15) sin 405° 15)

16) cos 103

16)

Find the exact value of the indicated trigonometric function of .

17) sin =5

3, cos =

23

Find cot . 17)

18) tan = -107

, in quadrant IIFind cos . 18)

19) sec =94

, in quadrant IV Find tan . 19)

Use the properties of the trigonometric functions to find the exact value of the expression.

20) sin2 80° + cos2 80° 20)

21) sec2 80° - tan2 80° 21)

2

22) tan 70° -sin 70°cos 70°

22)

Use the even-odd properties to find the exact value of the expression.

23) cos (-60°) 23)

24) sin -4

24)

Without graphing the function, determine its amplitude or period as requested.

25) y = -4 sin x Find the amplitude. 25)

26) y = cos 3x Find the period. 26)

27) y =56

cos (- 87

x) Find the period. 27)

Find an equation for the graph.28) 28)

A) y = 4 cos 12

x B) y = -4 cos (2x)

C) y = 4 cos (2x) D) y = 4 sin (2x)

3

29) 29)

A) y = -5 sin 13

x B) y = -5 sin (3x)

C) y = 5 cos 13

x D) y = -5 sin 23

x

Find the phase shift of the function.

30) y = 5 cos (6x + ) 30)

Write the equation of a sine function that has the given characteristics.

31) Amplitude: 3Period: 6

31)

32) Amplitude: 3Period: 4

Phase Shift:4

32)

Chapter 7

Find the exact value of the expression.

33) tan-1 (-1) 33)

34) sin-1 (0.5) 34)

35) csc-1 2 35)

4

36) sin (tan-1 2) 36)

37) cos [cos-1 (-0.9372)] 37)

38) cos sin-1 35

38)

39) tan cos-1 13

39)

Simplify the trigonometric expression by following the indicated direction.

40) Rewrite over a common denominator: 11 - cos

+1

1 + cos40)

41) Factor and simplify: 6 cos2 + 7 cos + 1cos2 - 1

41)

Simplify the expression as far as possible.

42) cos1 + sin

+ tan 42)

5

Complete the identity.

43) sin1 + sin

-sin

1 - sin= ? 43)

44) (sin + cos )21 + 2 sin cos

= ? 44)

45) cos - cos sin2 = ? 45)

46) sec4 + sec2 tan2 - 2 tan4 = ? 46)

6

47) csc (sin2 + cos2 tan )sin + cos

= ? 47)

Use Sum and Difference Formulas to find the exact value of the trigonometric function.

48) cos 512

48)

49) tan 345° 49)

Find the exact value of the expression.

50) sin 25° cos 35° + cos 25° sin 35° 50)

51) tan 70° + tan 80°1 - tan 70° tan 80°

51)

7

Complete the identity.

52) cos2

+ = ? 52)

53) cos ( - )sin cos

= ? 53)

Find the exact value under the given conditions.

54) sin =45

,2

< < ; cos =25

, 0 < <2

Find cos ( - ). 54)

55) tan =34

, < <32

; cos = -2425

,2

< < Find sin ( + ). 55)

8

Find the inverse function f-1 of the function f.

56) f(x) = 4 cos x + 5 56)

A) f-1(x) = cos-1 x - 54

B) f-1(x) = cos-1 x + 54

C) f-1(x) = sin x - 54

D) f-1(x) = 4 cos-1 x + 5

Find the domain of the function f and of its inverse function f-1.

57) f(x) = 4 sin(7x - 1) 57)

A) Domain of f: -17

, 17

Domain of f-1: ( , )

B) Domain of f: ( , )Domain of f-1: [-7, 7]

C) Domain of f: ( , )Domain of f-1: [-4, 4]

D) Domain of f: [-4, 4]Domain of f-1: ( , )

Use Double-Angle Formulas to find the exact value of the indicated trigonometric function overthe interval 0 2 .

58) csc = -32

, tan > 0 Find cos (2 ). 58)

59) sin =4 3

7, tan < 0 Find sin (2 ). 59)

9

Use the Half-angle Formulas to find the exact value of the trigonometric function.

60) sin 165° 60)

61) cos 512

61)

62) tan8

62)

Solve the equation on the interval 0 < 2 .

63) 2 cos (2 ) = 1 63)

64) 2 cos + 1 = 0 64)

10

65) 2 sin2 = sin 65)

66) cos = sin 66)

67) sin (2 ) + sin = 0 67)

Solve the problem.

68) For what numbers x, -2 x 2 , does the graph of y = csc x have verticalasymptotes?

68)

A) -32

, -2

,2

, 32

B) -2, -1, 0, 1, 2

C) -2 , - , 0, , 2 D) none

11

69) For what numbers x, -2 x 2 , does sec x = 1? 69)

A) -32

,2

B) -2 , 0, 2 C) - , D) none

70) What is the y-intercept of y = cot x? 70)

A)2

B) 0 C) 1 D) none

In the problem, sin and cos are given. Find the exact value of the indicated trigonometric function.

71) sin =14

, cos =154

Find tan . 71)

A) 4 B) 15 C) 1515

D) 4 1515

Chapter 14

Use the graph of y = g(x) to answer the questions.

72) Find the y-intercept(s), if any, of g. 72)

73) Find f(-1). 73)

74) Find f(1). 74)

12

75) Find f(2) 75)

76) Find f(-4). 76)

77) Find limx 1+

g(x). 77)

78) Does limx 4

g(x) exist? If it does, what is it? 78)

79) What is the domain of g? 79)

80) What is the range of g? 80)

81) Find limx 2+

g(x). 81)

82) Find limx 2-

g(x). 82)

83) Find limx 2

g(x). 83)

Find the limit algebraically.

84) lim -6x 3

84)

13

85) limx 1

2x - 74x + 5

85)

86) limx 0

x3 + 12x2 - 5x5x

86)

87) limx -3

x2 - 2x - 15x + 3

87)

88) limx 1

x4 - 1x - 1

88)

14

Find the limit as x approaches c of the average rate of change of the function from c to x.

89) c = 7; f(x) = 2x2 + 4 89)

90) c = 3; f(x) = 3x + 4 90)

15

Determine whether f is continuous at c.

91) f(x) =4

x2 - 8x; c = 0 91)

92) f(x) =x - 2

(x - 5)(x + 4); c = 0 92)

93) f(x) =3x - 6, x < 1

1, x = 16x - 3, x > 1

; c = 1 93)

Find the numbers at which f is continuous. At which numbers is f discontinuous?

94) f(x) =4x + 2x2 - 4

94)

16

Find the slope of the tangent line to the graph at the given point.95) f(x) = -3x + 11 at (2, 5) 95)

Find the equation of the tangent line to the graph of f at the given point.96) f(x) = 2x2 + x - 3 at x = (4, 33) 96)

Find the derivative of the function at the given value of x.97) f(x) = -5x - 7; x = 10 97)

17