542 CHAPTER 7 Analytic Trigonometry 66. ( ) ⎡ − − ⎣ ⎢ ⎤ ⎦ ⎥ − − tan sin 1 2 tan 3 4 1 1 67. ( ) ( ) ⎡ − + − ⎣ ⎢ ⎤ ⎦ ⎥ − − cos tan 1 cos 4 5 1 1 68. ( ) − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − sin 2 cos 3 5 1 69. ( ) − cos 2 tan 4 3 1 In Problems 70–81, solve each equation on the interval θ π ≤ < 0 2 . 70. θ = cos 1 2 71. θ + = tan 3 0 72. θ ( ) + = sin 2 1 0 73. θ ( ) = tan 2 0 74. θ = sec 4 2 75. θ = 0.2 sin 0.05 76. θ θ ( ) + = sin sin 2 0 77. θ θ θ ( ) − − + = sin 2 cos 2 sin 1 0 78. θ θ − + = 2sin 3sin 1 0 2 79. θ θ = + 4 sin 1 4 cos 2 80. θ θ ( ) = sin 2 2 cos 81. θ θ − = sin cos 1 In Problems 82–86, use a calculator to find an approximate value for each expression, rounded to two decimal places. 82. − sin 0.7 1 83. ( ) − − tan 2 1 84. ( ) − − cos 0.2 1 85. − sec 31 86. ( ) − − cot 4 1 In Problems 87–89, use a graphing utility to solve each equation on the interval π ≤ ≤ x 0 2 . Approximate any solutions rounded to two decimal places. 87. = x x 2 5 cos 88. + = x x x 2 sin 3 cos 4 89. = x x sin ln In Problems 90 and 91, find the exact solution of each equation. 90. π − = − x 3 sin 1 91. π + = − − x x 2 cos 4 cos 1 1 92. Use a Half-angle Formula to find the exact value of sin ° 15 . Then use a Difference Formula to find the exact value of sin ° 15 . Show that the answers you found are the same. 93. If you are given the value of θ cos and want the exact value of θ ( ) cos 2 , what form of the Double-angle Formula for θ ( ) cos 2 is most efficient to use? The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. In Problems 1–10, find the exact value of each expression. Express angles in radians. 1. ( ) − sec 2 3 1 2. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − sin 2 2 1 3. ( ) − − tan 3 1 4. − cos 01 5. − cot 11 6. ( ) − − csc 2 1 7. π ( ) − sin sin 11 5 1 8. ( ) − tan tan 7 3 1 9. ( ) − cot csc 10 1 10. ( ) ( ) − − sec cos 3 4 1 In Problems 11–14, use a calculator to evaluate each expression. Express angles in radians rounded to two decimal places. 11. − sin 0.382 1 12. − sec 1.4 1 13. − tan 31 14. − cot 51 In Problems 15–20 establish each identity. 15. θ θ θ θ θ θ θ θ + + = − − csc cot sec tan sec tan csc cot 16. θ θ θ θ + = sin tan cos sec 17. θ θ θ ( ) + = tan cot 2csc 2 18. sin tan tan cos cos α β α β α β ( ) + + = 19. θ θ θ ( ) = − sin 3 3 sin 4 sin3 20. θ θ θ θ θ − + = − tan cot tan cot 1 2cos2 Chapter Test
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