AN58 Answers: Chapter 7 59. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( )( ) ( )( ) ( )( ) + = − + = − + + + = − + + + = − + cos 2 1 sin 2 cos sin 1 2 sin cos cos sin cos sin sin cos 2 sin cos cos sin cos sin sin cos sin cos cos sin cos sin 2 2 2 2 θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ = − + = − + = − + cos sin sin cos sin sin cos sin sin sin cos sin sin sin cot 1 cot 1 61. θ θ θ θ = = + = + sec 2 1 cos 2 1 1 cos 2 2 1 cos 2 2 63. = = − + = + − = + − = + − = + ⋅ − = + − v v v v v v v v v v v v v v v v v v cot 2 1 tan 2 1 1 cos 1 cos 1 cos 1 cos 1 1 sec 1 1 sec sec 1 sec sec 1 sec sec 1 sec sec sec 1 sec 1 sec 1 2 2 65. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) − + = − − + + − + = + − − + + + − + = + ⋅ + = 1 tan 2 1 tan 2 1 1 cos 1 cos 1 1 cos 1 cos 1 cos 1 cos 1 cos 1 cos 1 cos 1 cos 2 cos 1 cos 1 cos 2 cos 2 2 67. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) − = − = − = = sin 3 sin cos 3 cos sin3 cos cos 3 sin sin cos sin 3 1 2 2 sin cos 2 sin 2 sin 2 2 69. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( ) ( ) ( ) = + = + − = + − − − = − + − − = − − tan 3 tan 2 tan tan 2 1 tan tan2 tan 2 tan 1 tan 1 tan 2 tan 1 tan tan tan 2 tan 1 tan 2 tan 3 tan tan 1 3 tan 2 2 3 2 2 3 2 71. θ θ θ θ ( ) ( ) ( ) ( ) − − = − = = 1 2 ln 1 cos 2 ln2 ln 1 cos 2 2 ln sin ln sin 1/2 2 1/2 73. π π π π { } 3 , 2 3 , 4 3 , 5 3 75. π π { } 0, 2 3 , 4 3 77. π π π π π π π { } 0, 3 , 2 , 2 3 , , 4 3 , 3 2 , 5 3 79. No real solution 81. π π π { } 0, 3 , , 5 3 83. 3 2 85. 7 25 87. 24 7 89. 24 25 91. 1 5 93. 25 7 95. π π π 0, 3 , , 5 3 97. π π 2 , 3 2 99. π π π π 2 , 7 6 , 3 2 , 11 6 101. (a) ( ) − − 11522 1152 in. or 1152 3 2 2 in. 2 2 (b) ( ) + + 162 2 162 cm or 162 3 2 2 cm 2 2 103. (a) θ θ θ θ θ θ θ θ ( ) ( ) = − = − = − = W D D D D 2 csc cot 2 1 sin cos sin 2 1 cos sin 2 tan 2 (b) θ = ° 24.45 105. (a) θ θ θ ( ) = − R v 2 16 cos sin cos 0 2 θ θ θ θ θ ( ) ( ) ( ) [ ] = − = − − v v 2 32 2 cos sin 2 cos 2 32 sin 2 cos 2 1 0 2 2 0 2 (b) π3 8 or ° 67.5 (c) ( ) − ≈ 32 2 2 18.75 ft (d) 45º 0 90º 20 θ = ° 67.5 π ( ) 3 8 radians makes R largest. = R 18.75 ft 107. θ θ θ ( ) ( ) = = = ⋅ = A h base h base s s s 1 2 1 2 cos 2 sin 2 1 2 sin 2 109. θ ( ) = + x x sin 2 4 4 2 111. − 1 4 113. α α α α α α α α α α α ( ) + = + = = = = ⋅ = z z 2 1 2 tan 2 1 tan 2 2 tan 2 sec 2 2 sin 2 cos 2 1 cos 2 2 sin 2 cos 2 sin 2 2 sin 2 2 2 2 115. y 1.25 x 2P 117. π π = − − = + + sin 24 2 4 4 6 2; cos 24 2 4 4 6 2 127. ( ) = + − − f x x x x 5 4 20 3 2 128. ( ) = + + −f x x x 5 3 2 1 1 129. { } { } { } − − = − − ≈ 2 ln3 7 ln2 ln2 ln3 ln9 ln128 ln2 ln3 6.548 130. 13 131. 1 6 132. = − + − + D x y x y 6 5 3 5 4 4 7.7 Assess Your Understanding (page 537) 1. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 1 2 3 2 1 3. − + ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 1 2 3 2 1 5. 2 2 7. θ θ ( ) ( ) [ ] − 1 2 cos 2 cos 6 9. θ θ ( ) ( ) [ ] + 1 2 sin 6 sin 2 11. θ θ ( ) ( ) [ ] + 1 2 cos 2 cos 8 13. θ θ ( ) [ ] − 1 2 cos cos 3 15. θ θ [ ( ) ] + 1 2 sin 2 sin 17. θ θ ( ) 2sin cos 3 19. θ θ ( ) 2cos 3 cos 21. θ θ ( ) 2sin 2 cos 23. θ θ 2 sin sin 2 119. θ θ θ θ θ θ θ θ ( ) ( ) ( ) ( ) + + ° + + ° = + ° + ° + ° + ° sin sin 120 sin 240 sin sin cos120 cos sin120 sin cos240 cos sin240 3 3 3 3 3 3 θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( ) [ ] ( ) ( ) ( ) = + − + ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ + − − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ = + − + − − + + + = − = − − = − = − sin 1 2 sin 3 2 cos 1 2 sin 3 2 cos sin 1 8 3 3 cos 9 cos sin 3 3 cos sin sin 1 8 sin 3 3 sin cos 9 sin cos 3 3 cos 3 4 sin 9 4 cos sin 3 4 sin 3 sin 1 sin 3 4 4 sin 3 sin 3 4 sin 3 from Example 2 3 3 3 3 3 2 2 3 3 2 2 3 3 2 3 2 3 121. − 1 2 123. = − y x 1 2 4 124. y x (21, 0) (3, 16) (0, 7) (7, 0) 125. + 3 1 2 126. y x 2 22 22 2 24 (24, 22) (22, 2) (0, 22) (2, 2) (4, 22) 4
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