C Challenge

Sketch each angle in standard position. Use the unit circle and a right triangle to find exact values of the cosine and the sine of the angle.

53. − 300 ° negative 300 degrees
54. 120°
55. 225°
56. − 780 ° negative 780 degrees
57. 1020°
58. Open-Ended Find the measures of four angles in standard position that have a sine of 0.5. (Hint: Use the unit circle and right triangles.)
59. Reasoning Suppose θ is an angle in standard position and cos θ = − 1 2 cosine theta equals negative , 1 half  and sin θ = − 3 2 . sine theta equals negative , fraction square root of 3 , over 2 end fraction . .  Can the value of θ be 60°? Can it be − 120 ° ? negative 120 degrees question mark  Draw a diagram and justify your reasoning.

Standardized Test Prep

SAT/ACT

60. Which angle, in standard position, is NOT coterminal with the others?
    1. − 570 ° negative 570 degrees
    2. − 170 ° negative 170 degrees
    3. 190°
    4. 550°
61. An angle drawn in standard position has a terminal side that passes through the point ( 2 , − 2 ) . square root of 2 comma minus square root of 2 close .  What is one possible measure of the angle?
    6. 45°
    7. 225°
    8. 315°
    9. 330°
62. An angle of 120° is in standard position. What are the coordinates of the point at which the terminal side intersects the unit circle?
    1. ( 1 2 , 3 2 ) open . 1 half , comma , fraction square root of 3 , over 2 end fraction . close
    2. ( − 1 2 , 3 − 2 ) open . negative , 1 half , comma , fraction square root of 3 , over negative 2 end fraction . close
    3. ( − 3 2 , 1 2 ) open . fraction negative square root of 3 , over 2 end fraction , comma , 1 half . close
    4. ( − 1 2 , 3 2 ) open . negative , 1 half , comma , fraction square root of 3 , over 2 end fraction . close

Short Response

63. Use an angle in standard position to find the exact value of [ sin ( − 135 ° ) ] 2 + [ cos ( − 135 ° ) ] 2 . left bracket sine open negative 135 degrees close right bracket squared . plus . left bracket cosine open negative 135 degrees close right bracket squared . .  Show your work.

Mixed Review

Determine whether each function is or is not periodic. If it is, find the period. See Lesson 13-1.

Find the foci of each hyperbola. Draw the graph. See Lesson 10-5.

67. y 2 16 − x 2 4 = 1 fraction y squared , over 16 end fraction , minus , fraction x squared , over 4 end fraction , equals 1
68. y 2 25 − x 2 100 = 1 fraction y squared , over 25 end fraction , minus . fraction x squared , over 100 end fraction . equals 1
69. x 2 36 − y 2 49 = 1 fraction x squared , over 36 end fraction , minus , fraction y squared , over 49 end fraction , equals 1
70. x 2 81 − y 2 64 = 1 fraction x squared , over 81 end fraction , minus , fraction y squared , over 64 end fraction , equals 1

Get Ready! To prepare for Lesson 13-3, do Exercises 71–74.

Find the area of a circle with the given radius or diameter. Use 3.14 for π. See p. 968.

71. radius 4 in.
72. diameter 70 m
73. radius 8 mi
74. diameter 3.4 ft

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