616 CHAPTER 6 The Circular Functions and Their Graphs Concept Check The figure displays a unit circle and an angle of 1 radian. The tick marks on the circle are spaced at every two-tenths radian. Use the figure to estimate each value. 3 5 6 0.4 radian 0.2 radian x y 0.6 0.2 0.4 0.6 0.8 0.2 1 radian 0.8 radian 0.6 radian 2 4 47. cos 0.8 48. cos 0.6 49. sin 2 50. sin 5.4 51. sin 3.8 52. cos 3.2 53. a positive angle whose cosine is -0.65 54. a positive angle whose sine is -0.95 55. a positive angle whose sine is 0.7 56. a positive angle whose cosine is 0.3 Concept Check Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that p≈3.14.) 57. cos 2 58. sin1-12 59. sin 5 60. cos 6 61. tan 6.29 62. tan1-6.292 Find the approximate value of s, to four decimal places, in the interval C 0, p 2 D that makes each statement true. See Example 4(a). 63. tans = 0.2126 64. cos s = 0.7826 65. sins = 0.9918 66. cot s = 0.2994 67. sec s = 1.0806 68. csc s = 1.0219 Find the exact values of s in the given interval that satisfy the given condition. 75. 30, 2p2; sins = - 23 2 76. 30, 2p2; cos s = - 1 2 77. 30, 2p2; cos2 s = 1 2 78. 30, 2p2; tan2 s = 3 79. 3-2p, p2; 3 tan2 s = 1 80. 3-p, p2; sin2 s = 1 2 Find the exact value of s in the given interval that has the given circular function value. See Example 4(b). 69. c p 2 , pd ; sins = 1 2 70. c p 2 , pd ; cos s = - 1 2 71. c p, 3p 2 d ; tans = 23 72. c p, 3p 2 d ; sins = - 1 2 73. c 3p 2 , 2pd ; tans = -1 74. c 3p 2 , 2pd ; cos s = 3 2
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