A-38 Answers to Selected Exercises 7.6 Exercises 1. Ep 3 , 5p 3 F 3. E 7p 6 , 11p 6 F 5. 5270°6 7. E p 6 , 5p 6 , 7p 6 , 11p 6 F 9. E7p 12 , 11p 12 , 19p 12 , 23p 12 F 11. ∅ 13. -30° is not in the interval 30°, 360°2. 15. E3p 4 , 7p 4 F 17. E p 6 , 5p 6 F 19. ∅ 21. Ep 4 , 2p 3 , 5p 4 , 5p 3 F 23. 5p6 25. E7p 6 , 3p 2 , 11p 6 F 27. 530°, 210°, 240°, 300°6 29. 590°, 210°, 330°6 31. 545°, 135°, 225°, 315°6 33. 545°, 225°6 35. 50°, 30°, 150°, 180°6 37. 50°, 45°, 135°, 180°, 225°, 315°6 39. 553.6°, 126.4°, 187.9°, 352.1°6 41. 5149.6°, 329.6°, 106.3°, 286.3°6 43. ∅ 45. 557.7°, 159.2°6 47. 5180° + 360°n, where n is any integer6 49. Ep 3 + 2np, 2p 3 + 2np, where n is any integerF 51. 519.5° + 360°n, 160.5° + 360°n, 210° + 360°n, 330° + 360°n, where n is any integer6 53. Ep 3 + 2np, p+ 2np, 5p 3 + 2np, where n is any integerF 55. 5180°n, where n is any integer6 57. 50.8751 + 2np, 2.2665 + 2np, 3.5908 + 2np, 5.8340 + 2np, where n is any integer6 59. 533.6° + 360°n, 326.4° + 360°n, where n is any integer6 61. 545° + 180°n, 108.4° + 180°n, where n is any integer6 63. 50.6806, 1.41596 65. Ep 3 , p, 4p 3 F 67. 560°, 210°, 240°, 310°6 69. E p 12 , 11p 12 , 13p 12 , 23p 12 F 71. 590°, 210°, 330°6 73. E p 18 , 7p 18 , 13p 18 , 19p 18 , 25p 18 , 31p 18 F 75. 567.5°, 112.5°, 247.5°, 292.5°6 77. Ep 2 , 3p 2 F 79. E0, p 3 , p, 5p 3 F 81. ∅ 83. 5180°6 85. E p 3 , p, 5p 3 F 87. E p 12 + 2np 3 , p 4 + 2np 3 , where n is any integerF 89. 5720°n, where n is any integer6 91. E2p 3 + 4np, 4p 3 + 4np, where n is any integerF 93. 530° + 360°n, 150° + 360°n, 270° + 360°n, where n is any integer6 95. Enp, p 6 + 2np, 5p 6 + 2np, where n is any integerF 97. 51.3181 + 2np, 4.9651 + 2np, where n is any integer6 99. 511.8° + 180°n, 78.2° + 180°n, where n is any integer6 101. 530° + 180°n, 90° + 180°n, 150° + 180°n, where n is any integer6 103. 51.28026 105. (a) 0.00164 and 0.00355 (b) 30.00164, 0.003554 (c) outward 107. (a) 1 4 sec (b) 1 6 sec (c) 0.21 sec 109. (a) See the graph in the text. (b) The graph is periodic, and the wave has “jagged square” tops and bottoms. (c) This will occur when t is in one of these intervals: 10.0045, 0.00912, 10.0136, 0.01822, 10.0227, 0.02732. 105. tan x 2 + cot x 2 cot x 2 - tan x 2 = sec x 107. a = -885.6; c = 885.6; v = 240p 109. 106° 111. 2 7.5 Exercises 1. one; one 3. cos y 5. p 7. (a) 3-1, 14 (b) C - p 2 , p 2 D (c) increasing (d) -2 is not in the domain. 9. (a) 1-∞, ∞2 (b) A - p 2 , p 2 B (c) increasing (d) no 11. The interval must be chosen so that the function is oneto-one, and the sine and cosine functions are not one-to-one on the same intervals. 13. 0 15. p 17. p 4 19. 0 21. - p 3 23. 5p 6 25. sin-1 23 does not exist. 27. 3p 4 29. - p 6 31. p 6 33. 0 35. csc-1 22 2 does not exist. 37. -45° 39. -60° 41. 120° 43. 120° 45. -30° 47. sin-1 2 does not exist. 49. -7.6713835° 51. 113.500970° 53. 30.987961° 55. 121.267893° 57. -82.678329° 59. 1.1900238 61. 1.9033723 63. 0.83798122 65. 2.3154725 67. 2.4605221 69. –4 0 p 4 y = sec–1 x 71. –4 0 p 4 y = cot–1 x 73. –2 2 x y 0 P y = arcsec x1 2 P 2 75. 27 3 77. 25 5 79. 120 169 81. - 7 25 83. 426 25 85. 2 87. 63 65 89. 210 - 3230 20 91. 0.894427191 93. 0.1234399811 95. 21 - u2 97. 21 - u2 99. 4 2u2 - 4 u2 101. u22 2 103. 224 - u2 4 - u2 105. 41° 107. (a) 18° (b) 18° (c) 15° (e) 1 0 10 1.414213 m (Note: Because of the computational routine, there may be a discrepancy in the last few decimal places.) (f) 22 109. 44.7% 111. In each case, the result is x. 112. In each case, the result is x. The graph is that of the line y = x. 113. 114. –10 –10 10 10 y = tan(tan–1 x) It is also the graph of y = x. –10 –10 10 10 y = tan–1(tan x) It does not agree because the range of the inverse tangent function is A - p 2 , p 2 B, not 1-∞, ∞2, as was the case in Exercise 113.
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