C Challenge

Use a graphing calculator to graph each function in the interval from 0 to 2π. Then sketch each graph.

49. y = sin x + x y equals sine x plus x
50. y = sin x + 2 x y equals sine x plus 2 x
51. y = cos x − 2 x y equals cosine x minus 2 x
52. y = cos x + x y equals cosine x plus x
53. y = sin ( x + cos x ) y equals sine open x plus cosine x close
54. y = sin ( x + 2 cos x ) y equals sine open x plus 2 cosine x close

Standardized Test Prep

SAT/ACT

55. Which function is a phase shift of y = sin θ y equals sine theta  by 5 units to the left?
    1. y = 5 sin θ y equals 5 sine theta
    2. y = sin θ + 5 y equals sine theta plus 5
    3. y = sin ( θ + 5 ) y equals sine open theta plus 5 close
    4. y = sin 5 θ y equals sine 5 theta
56. Which function is a translation of y = cos θ y equals cosine theta  by 5 units down?
    6. y = − 5 cos θ y equals negative 5 cosine theta
    7. y = cos θ − 5 y equals cosine theta negative 5
    8. y = cos ( θ − 5 ) y equals cosine open theta negative 5 close
    9. y = cos ( − 5 θ ) y equals cosine open negative 5 theta close
57. Which function is a translation of y = sin θ y equals sine theta  that is π 3 pi over 3  units up and π 2 pi over 2  units to the left?
    1. y = sin ( θ + π 3 ) + π 2 y equals sine . open . theta plus , pi over 3 . close . plus , pi over 2
    2. y = sin ( θ + π 2 ) + π 3 y equals sine . open . theta plus , pi over 2 . close . plus , pi over 3
    3. y = sin ( θ − π 2 ) + π 3 y equals sine . open . theta minus , pi over 2 . close . plus , pi over 3
    4. y = sin ( θ − π 3 ) − π 2 y equals sine . open . theta minus , pi over 3 . close . minus , pi over 2

Short Response

58. Find values of a and b such that the function y = sin θ y equals sine theta  can be expressed as y = a cos ( θ + b ) . y equals eh cosine open theta plus b close .

Mixed Review

Identify the period of each function. Then tell where two asymptotes occur for each function. See Lesson 13-6.

59. y = tan 6 θ y equals tangent 6 theta
60. y = tan θ 4 y equals tangent , theta over 4
61. y = tan 1 . 5 θ y equals tangent 1 . 5 theta
62. y = tan θ 6 y equals tangent , theta over 6

For the given probability of success P on each trial, find the probability of x successes in n trials. See Lesson 11-8.

63. x = 4 , n = 5 , p = 0 . 2 x equals 4 comma n equals 5 comma p equals 0 . 2
64. x = 3 , n = 5 , p = 0 . 6 x equals 3 comma n equals 5 comma p equals 0 . 6
65. x = 4 , n = 8 , p = 0 . 7 x equals 4 comma n equals 8 comma p equals 0 . 7
66. x = 7 , n = 8 , p = 0 . 7 x equals 7 comma n equals 8 comma p equals 0 . 7

Get Ready! To prepare for Lesson 13-8, do Exercises 67–71. See p. 965.

Find the reciprocal of each fraction.

67. 9 13 9 thirteenths
68. − 5 8 negative 5 over 8
69. 1 2 π fraction 1 , over 2 pi end fraction
70. 4 m 15 fraction 4 m , over 15 end fraction
71. 14 − t 14 over negative t

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