500 CHAPTER 7 Analytic Trigonometry 67. θ θ θ − = + sin cos 1 cos 2 2 68. θ θ θ − + = cos sin sin 0 2 2 69. θ θ ( ( ) ) = − + sin 6 cos 1 2 70. θ θ ( ) ( ) = − − 2 sin 3 1 cos 2 71. θ θ ( ) = − − cos sin 72. θ θ ( ) − − = cos sin 0 73. θ θ = tan 2 sin 74. θ θ = tan cot 75. θ θ + = 1 sin 2cos2 76. θ θ = + sin 2cos 2 2 77. θ θ − + = 2sin 5sin 3 0 2 78. θ θ − − = 2cos 7cos 4 0 2 79. θ θ ( ) − = 3 1 cos sin2 80. θ θ ( ) + = 4 1 sin cos2 81. θ θ = tan 3 2 sec 2 82. θ θ = + csc cot 1 2 83. θ θ + = sec tan 0 2 84. θ θ θ = + sec tan cot In Problems 85–96, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places. 85. + = x x 5cos 0 86. − = x x 4 sin 0 87. − = x x 22 17 sin 3 88. + = x x 19 8cos 2 89. + = x x x sin cos 90. − = x x x sin cos 91. − = x x 2 cos 0 2 92. + = x x 3 sin 0 2 93. ( ) − = x x x 2 sin 2 3 2 94. ( ) = + x x x 3cos 2 2 95. − = > x e x 6 sin 2, 0 x 96. ( ) − = > x e x 4cos 3 1, 0 x 97. Mixed Practice What are the zeros of ( ) = − f x x 4 sin 3 2 on the interval π [ ] 0, 2 ? 98. Mixed Practice What are the zeros of ( ) ( ) = + f x x 2cos 3 1 on the interval π [ ] 0, ? 99. Mixed Practice ( ) = f x x 3sin (a) Find the zeros of f on the interval π π [ ] −2 , 4 . (b) Graph ( ) = f x x 3sin on the interval π π [ ] −2 , 4 . (c) Solve ( ) = f x 3 2 on the interval π π [ ] −2 , 4 . What points are on the graph of f ? Label these points on the graph drawn in part (b). (d) Use the graph drawn in part (b) along with the results of part (c) to determine the values of x such that ( ) > f x 3 2 on the interval π π [ ] −2 , 4 . 100. Mixed Practice ( ) = f x x 2cos (a) Find the zeros of f on the interval π π [ ] −2 , 4 . (b) Graph ( ) = f x x 2cos on the interval π π [ ] −2 , 4 . (c) Solve ( ) = − f x 3 on the interval π π [ ] −2 , 4 . What points are on the graph of f ? Label these points on the graph drawn in part (b). (d) Use the graph drawn in part (b) along with the results of part (c) to determine the values of x such that ( ) <− f x 3 on the interval π π [ ] −2 , 4 . 101. Mixed Practice ( ) = f x x 4 tan (a) Solve ( ) = − f x 4. (b) For what values of x is ( ) <− f x 4 on the interval π π ( ) − 2 , 2 ? 102. Mixed Practice ( ) = f x x cot (a) Solve ( ) = − f x 3. (b) For what values of x is ( ) >− f x 3 on the interval π ( ) 0, ? 103. Mixed Practice (a) Graph ( ) ( ) = + f x x 3sin 2 2 and ( ) = g x 7 2 on the same Cartesian plane for the interval π [ ] 0, . (b) Solve ( ) ( ) = f x g x on the interval π [ ] 0, , and label the points of intersection on the graph drawn in part (a). (c) Solve ( ) ( ) > f x g x on the interval π [ ] 0, . (d) Shade the region bounded by ( ) ( ) = + f x x 3sin 2 2 and ( ) = g x 7 2 between the two points found in part (b) on the graph drawn in part (a). 104. Mixed Practice (a) Graph ( ) = + f x x 2 cos 2 3 and ( ) = g x 4 on the same Cartesian plane for the interval π [ ] 0, 4 . (b) Solve ( ) ( ) = f x g x on the interval π [ ] 0, 4 , and label the points of intersection on the graph drawn in part (a). (c) Solve ( ) ( ) < f x g x on the interval π [ ] 0, 4 . (d) Shade the region bounded by ( ) = + f x x 2cos 2 3 and ( ) = g x 4 between the two points found in part (b) on the graph drawn in part (a). 105. Mixed Practice (a) Graph ( ) = − f x x 4cos and ( ) = + g x x 2cos 3 on the same Cartesian plane for the interval π [ ] 0, 2 . (b) Solve ( ) ( ) = f x g x on the interval π [ ] 0, 2 , and label the points of intersection on the graph drawn in part (a). (c) Solve ( ) ( ) > f x g x on the interval π [ ] 0, 2 . (d) Shade the region bounded by ( ) = − f x x 4cos and ( ) = + g x x 2cos 3 between the two points found in part (b) on the graph drawn in part (a). 106. Mixed Practice (a) Graph ( ) = f x x 2sin and ( ) = − + g x x 2sin 2 on the same Cartesian plane for the interval π [ ] 0, 2 . (b) Solve ( ) ( ) = f x g x on the interval π [ ] 0, 2 , and label the points of intersection on the graph drawn in part (a). (c) Solve ( ) ( ) > f x g x on the interval π [ ] 0, 2 . (d) Shade the region bounded by ( ) = f x x 2sin and ( ) = − + g x x 2sin 2 between the two points found in part (b) on the graph drawn in part (a).
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