C Challenge

The given angle θ is in standard position. Find the radian measure of the angle that results after the given number of revolutions from the terminal side of θ.

51. θ = π 2 ; theta equals , pi over 2 , semicolon  1 clockwise revolution
52. θ = − 2 π 3 ; theta equals negative , fraction 2 pi , over 3 end fraction , semicolon  1 counterclockwise revolution
53. Reasoning Use the proportion measure of central angle length of intercepted arc = measure of one complete rotation circumference cap usetheproportion . fraction measureofcentralangle , over lengthofinterceptedarc end fraction . equals . fraction measureofonecompleterotation , over circumference end fraction  to derive the formula s = r θ . s equals r theta .  Use θ for the central angle measure and s for the arc length. Measure the rotation in radians.

Standardized Test Prep

SAT/ACT

54. Which pairs of measurements represent the same angle measures?
    1. 240 ° , 7 π 6  radians 240 degrees comma , fraction 7 pi , over 6 end fraction . radians
    2. 135 ° , 3 π 4  radians 135 degrees comma , fraction 3 pi , over 4 end fraction . radians
    3. 150 ° , 5 π 6  radians 150 degrees comma , fraction 5 pi , over 6 end fraction . radians
    1. I and II only
    2. I and III only
    3. II and III only
    4. I, II, and III
55. What is the exact value of cos ( 5 π 4  radians ) ? cosine . open . fraction 5 pi , over 4 end fraction . radians . close . question mark
    6. − 3 2 negative , fraction square root of 3 , over 2 end fraction
    7. − 2 2 negative , fraction square root of 2 , over 2 end fraction
    8. − 1 2 negative , 1 half
    9. 2 2 fraction square root of 2 , over 2 end fraction
56. Two arcs have the same length. One arc is intercepted by an angle of 3 π 2  radians fraction 3 pi , over 2 end fraction . radians  in a circle of radius 15 cm. If the radius of the other circle is 25 cm, what central angle intercepts the arc?
    1. 3 π 2  radians fraction 3 pi , over 2 end fraction . radians
    2. 9 π 10  radians fraction 9 pi , over 10 end fraction . radians
    3. 5 π 2  radians fraction 5 pi , over 2 end fraction . radians
    4. 5 π 3  radians fraction 5 pi , over 3 end fraction . radians

Short Response

57. For a central angle of one radian, describe the relationship between the radius of the circle and the length of the arc.

Mixed Review

Sketch each angle in standard position. See Lesson 13-2.

58. 15°
59. − 75 ° negative 75 degrees
60. 150°
61. − 270 ° negative 270 degrees
62. − 85 ° negative 85 degrees

Find the mean and the standard deviation for each set of values. See Lesson 11-6.

63. 12 13 15 9 16 5 18 16 12 11 15
64. 21 29 35 26 25 28 27 51 24 34

Get Ready! To prepare for Lesson 13-4, do Exercises 65–67.

Use the graph. Find the value(s) of each of the following. See Lesson 13-1.

65. the period
66. the domain
67. the amplitude

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