Sound For sound waves, the period and the frequency of a pitch are reciprocals of each other: period = seconds cycle period , equals . fraction seconds , over cycle end fraction  and frequency = cycles second . frequency . equals . fraction cycles , over second end fraction . .  Write an equation for each pitch. Let θ = time in seconds. Use a = eh equals  1.

49. the lowest pitch easily heard by humans: 30 cycles per second
50. the lowest pitch heard by elephants: 15 cycles per second
51. the highest pitch heard by bats: 120,000 cycles per second

Find the period and amplitude of each function. Sketch each function from 0 to 2π.

52. y = sin ( θ + 2 ) y equals sine open theta plus 2 close
53. y = sin ( θ − 3 ) y equals sine open theta negative 3 close
54. y = sin ( 2 θ + 4 ) y equals sine open 2 theta plus 4 close

Standardized Test Prep

SAT/ACT

55. Which value is NOT the same as the other three values?
    1. sin 100 ° sine , 100 degrees
    2. sin 80 ° sine , 80 degrees
    3. sin − 80 ° negative 80 degrees
    4. sin − 260 ° negative 260 degrees
56. What is the amplitude of y = 3 sin 4 θ ? y equals 3 sine 4 theta question mark
    6. 4 3 4 thirds
    7. 3
    8. 4
    9. 2π
57. Which answer choice describes y = − sin 2 θ ? y equals negative sine 2 theta question mark
    1. amplitude − 2 , negative 2 comma  period 4π
    2. amplitude 2, period − π negative pi
    3. amplitude 1, period π
    4. amplitude 2π, period 1
58. Which function has a period of 4π and an amplitude of 8?
    6. y = − 8 sin 8 θ y equals negative 8 sine 8 theta
    7. y = − 8 sin 1 2 θ y equals negative 8 sine , 1 half , theta
    8. y = 8 sin 2 θ y equals 8 sine 2 theta
    9. y = 4 sin 8 θ y equals 4 sine 8 theta

Short Response

59. Find the value of θ that is between 90° and 180° such that sin θ = sin 60 ° . sine theta equals sine , 60 degrees .  Show your work.

Mixed Review

Write each measure in radians. Express the answer in terms of π and as a decimal rounded to the nearest hundredth. See Lesson 13-3.

60. − 80 ° negative 80 degrees
61. 150°
62. − 240 ° negative 240 degrees
63. 320°
64. − 450 ° negative 450 degrees
65. A poll of teenagers in one town showed that 43% play a team sport. It also showed that 21% play varsity team sports. Find the probability that a teenager plays varsity sports, given that the teenager plays a team sport. See Lesson 11-4.

Get Ready! To prepare for Lesson 13-5, do Exercises 66–69.

Find the x-coordinate of each point on the unit circle below. See Lesson 13-2.

66. A
67. B
68. C
69. D

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