AN54 Answers: Chapter 7 7.3 Assess Your Understanding (page 498) 7. F 8. T 9. T 10. F 11. d 12. a 13. 7 6 , 11 6 π π { } 15. 7 6 , 11 6 π π { } 17. 3 4 , 7 4 π π { } 19. 2 3 , 4 3 π π { } 21. 3 4 , 5 4 π π { } 23. 3 , 2 3 , 4 3 , 5 3 π π π π { } 25. 4 , 3 4 , 5 4 , 7 4 π π π π { } 27. 2 , 7 6 , 11 6 π π π { } 29. 3 , 2 3 , 4 3 , 5 3 π π π π { } 31. 4 9 , 8 9 , 16 9 π π π { } 33. 3 4 , 7 4 π π { } 35. 11 6 π { } 37. k k 6 2 , 5 6 2 ; 6 , 5 6 , 13 6 , 17 6 , 25 6 , 29 6 θ θ π π θ π π π π π π π π { } = + = + 39. k 5 6 ; 5 6 , 11 6 , 17 6 , 23 6 , 29 6 , 35 6 θ θ π π π π π π π π { } = + 41. k k 2 2 , 3 2 2 ; 2 , 3 2 , 5 2 , 7 2 , 9 2 , 11 2 θ θ π π θ π π π π π π π π { } = + = + 43. k 6 ; 6 , 7 6 , 13 6 , 19 6 , 25 6 , 31 6 θ θ π π π π π π π π { } { } = + 45. k k 3 , 2 3 ; 3 , 2 3 , 4 3 , 5 3 , 7 3 , 8 3 θ θ π π θ π π π π π π π π { } = + = + 47. k k 8 3 4 , 10 3 4 ; 8 3 , 10 3 , 20 3 , 22 3 , 32 3 , 34 3 θ θ π π θ π π π π π π π π { } = + = + 49. 0.41, 2.73 { } 51. 1.37, 4.51 { } 53. 2.69, 3.59 { } 55. 1.82, 4.46 { } 57. 2.08, 5.22 { } 59. 0.73, 2.41 { } 61. 2 , 2 3 , 4 3 , 3 2 π π π π { } 63. 2 , 7 6 , 11 6 π π π { } 65. 0, 4 , 5 4 π π { } 67. 2 , 2 3 , 4 3 , 3 2 π π π π { } 69. π{ } 71. 4 , 5 4 π π { } 73. 0, 3 , , 5 3 π π π { } 75. 6 , 5 6 , 3 2 π π π { } 77. 2 π{ } 79. 0{ } 81. 3 , 5 3 π π { } 83. No real solution 85. 1.31, 1.98, 3.84 { } − 87. 0.52 { } 89. 1.26 { } 91. 1.02, 1.02 { } − 93. 0, 2.15 { } 95. 0.76, 1.35 { } 97. 3 , 2 3 , 4 3 , 5 3 π π π π 99. (a) 2 , ,0, ,2 ,3 ,4 π π π π π π − − (b) y 3.75 x 5P 6 , 3P P 6 3 2 3 2 13P 6 , 3 2 17P 6 , 3 2 11P 6 , 3 2 , 2 7P 6 , 3 2 2 (c) 11 6 , 7 6 , 6 , 5 6 , 13 6 , 17 6 π π π π π π { } − − (d) π π π π π π { } − < <− < < < < x x x x 11 6 7 6 or 6 5 6 or 13 6 17 6 101. (a) x x k k 4 , aninteger π π { } = − + (b) x 2 4 π π − < <− or 2 , 4 π π ( ) − − 103. (a), (d) y 7 x P 5P 12 , 7 2 P 12 , 7 2 g(x) 5 7 2 f(x) 5 3 sin(2x) 1 2 (b) 12 , 5 12 π π { } (c) π π π π { } ( ) < < x x 12 5 12 or 12 , 5 12 105. (a), (d) y 5 x 2P g(x) 5 2 cos x 1 3 f(x) 5 24 cos x 4P 3 , 2 2P 3 , 2 (b) 2 3 , 4 3 π π { } (c) x x 2 3 4 3 π π { } < < or 2 3 , 4 3 π π ( ) 107. (a) 0 sec, 0.43 sec, 0.86 sec, (b) 0.21 sec (c) [ ] [ ] [ ] ∪ ∪ 0, 0.03 0.39, 0.43 0.86, 0.89 109. (a) 150 mi (b) 6.06, 8.44, 15.72, 18.11 min (c) Before 6.06 min, between 8.44 and 15.72 min, and after 18.11 min (d) No 111. 2.03, 4.91 113. (a) ° ° 30 , 60 (b) 123.6 m (c) 0º 0 90º 130 115. ° 28.90 117. Yes; it varies from 1.25 to 1.34. 119. 1.47 121. θ = ° 48.8 B 123. θ θ π π { } = + k k 5 6 , where is any integer 127. = x y log6 128. − + 9 17 4 , 9 17 4 129. θ θ θ θ = − = − = = − tan 1 3 ; csc 10; sec 10 3 ; cot 3 130. Amplitude: 2 Period: π Phase shift: π 2 y x 3P 2.5 131. { } ( ) > ∞ x x 3 or 3, 132. π ≈ 3 cm 9.425 cm 133. = a 6 134. odd 135. = − + y x 5 2 21 2 136. π − 2 3 7.4 Assess Your Understanding (page 508) 3. identity; conditional 4. −1 5. 0 6. T 7. F 8. T 9. c 10. b 11. θ 1 cos 13. θ θ +1 sin cos 15. θ θ 1 sin cos 17. 2 19. θ θ + + 3 sin 1 sin 1 21. θ θ θ θ θ θ θ ⋅ = ⋅ = = csc cos 1 sin cos cos sin cot 23. θ θ θ θ ( ) ( ) + − = + − = + = 1 tan 1 tan 1 tan sec 2 2 2 2 25. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( ) ( ) + = + = + = = = cos tan cot cos sin cos cos sin cos sin cos cos sin cos 1 cos sin 1 sin csc 2 2 27. − = ⋅ − = − = u u u u u u u u tan cot cos tan 1 tan cos 1 cos sin 2 2 2 2 29. θ θ θ θ ( )( ) − + = − = sec 1 sec 1 sec 1 tan 2 2 31. θ θ θ θ θ θ ( )( ) + − = − = sec tan sec tan sec tan 1 2 2 33. θ θ θ θ θ θ ( ) + = = ⋅ = cos 1 tan cos sec cos 1 cos 1 2 2 2 2 2 2 35. θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) + + − = + + + − + sin cos sin cos sin 2 sin cos cos sin 2 sin cos cos 2 2 2 2 2 2 θ θ θ θ = + + + = + = sin cos sin cos 1 1 2 2 2 2 2 37. θ θ θ θ θ θ θ θ ( ) ( ) − = − = + = + sec sec sec sec 1 1tan tan tan tan 4 2 2 2 2 2 4 2 39. ( ) ( ) − = − = − ⋅ + + = − + = + = + u u u u u u u u u u u u u u u u u sec tan 1 cos sin cos 1 sin cos 1 sin 1 sin 1 sin cos 1 sin cos cos 1 sin cos 1 sin 2 2 41. θ θ θ θ θ θ θ θ θ ( ) + = + + = + + = + 3 sin 4 cos 3 sin 3 cos cos 3 sin cos cos 3 cos 2 2 2 2 2 2 2 2 2 43. 1 cos 1 sin 1 1 sin 1 sin 1 1 sin 1 sin 1 sin 1 1 sin sin 2 2 θ θ θ θ θ θ θ θ θ ( )( ) ( ) − + = − − + = − + − + = − − =
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