A-31 Answers to Selected Exercises 79. - 22 2 ; - 22 2 ; 1; 1; - 22 ; -22 81. 23 2 ; 1 2 ; 23 ; 23 3 ; 2; 223 3 83. - 1 2 ; - 23 2 ; 23 3 ; 23 ; - 2 23 3 ; -2 85. 1 2 ; - 23 2 ; - 23 3 ; - 23 ; - 2 23 3 ; 2 87. - 23 2 ; 1 2 ; - 23 ; - 23 3 ; 2; - 223 3 89. - 22 2 91. - 23 2 93. - 22 95. -1 97. 30°; 150° 99. 120°; 300° 101. 45°; 315° 103. 210°; 330° 105. 30°; 210° 107. 225°; 315° In Exercises 109–121, the number of decimal places may vary depending on the calculator used. We show six places. 109. 0.625243 111. 1.027349 113. 15.055723 115. 0.740805 117. 1.483014 119. tan 23.4° ≈0.432739 121. cot 77° ≈0.230868 123. 55.845496° 125. 16.166641° 127. 38.491580° 129. 68.673241° 131. 45.526434° 133. 12.227282° 135. 70 lb 137. -2.9° 139. 2500 lb 141. A 2200-lb car on a 2° uphill grade has greater grade resistance. 143. 703 ft 145. R would decrease; 644 ft, 1559 ft 147. A: 69 mph; B: 66 mph Chapter 5 Quiz [5.1] 1. (a) 71° (b) 161° 2. 65°; 115° 3. 26°; 64° 4. (a) 77.2025° (b) 22° 01′ 30″ 5. (a) 50° (b) 300° (c) 170° (d) 417° 6. 1800° [5.2] 7. sin u = 7 25 ; cos u = - 24 25 ; tan u = - 7 24 ; cot u = - 24 7 ; sec u = - 25 24 ; csc u = 25 7 [5.3] 8. sin A = 3 5 ; cos A = 4 5 ; tan A = 3 4 ; cot A = 4 3 ; sec A = 5 4 ; csc A = 5 3 9. U sin U cos U tan U cot U sec U csc U 30° 1 2 23 2 23 3 23 223 3 2 45° 22 2 22 2 1 1 2 22 60° 23 2 1 2 23 23 3 2 223 3 10. = 3x2 sin u 11. w = 18 ; x = 1823 ; y = 18 ; z = 1822 In Exercises 12–14, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 12. 22 2 ; - 22 2 ; -1; -1; - 22 ; 22 13. - 1 2 ; - 23 2 ; 23 3 ; 23 ; - 2 23 3 ; -2 14. - 23 2 ; 1 2 ; - 23 ; - 23 3 ; 2; - 223 3 15. 60°; 120° 16. 135°; 225° 17. 0.673013 18. -1.181763 19. 69.497888° 20. 24.777233° 5.4 Exercises 1. B 3. A 5. C 7. C 9. A 11. E 13. 23.865 to 23.875 Note to student: While most of the measures resulting from solving triangles in this chapter are approximations, for convenience we use =rather than ?. 15. B = 53° 40′; a = 571 m; b = 777 m 17. M= 38.8°; n = 154 m; p = 198 m 19. A = 47.9108°; c = 84.816 cm; a = 62.942 cm 21. A = 37° 40′ ; B = 52° 20′ ; c = 20.5 ft 23. B = 62.0°; a = 8.17 ft; b = 15.4 ft 25. A = 17.0°; a = 39.1 in.; c = 134 in. 27. B = 29.0°; a = 70.7 cm; c = 80.9 cm 29. A = 36°; B = 54° ; b = 18 m 31. c = 85.9 yd; A = 62° 50′ ; B = 27° 10′ 33. b = 42.3 cm; A = 24° 10′ ; B = 65° 50′ 35. B = 36° 36′ ; a = 310.8 ft; b = 230.8 ft 37. A = 50° 51′ ; a = 0.4832 m; b = 0.3934 m 39. 9.35 m 41. 128 ft 43. 26.92 in. 45. 28.0 m 47. 13.3 ft 49. 37° 35′ 51. 42.18° 53. 22° 55. (a) 29,000 ft (b) shorter 57. 270°; N 90° W, or S 90° W 59. 0°; N 0° E, or N 0° W 61. 315°; N 45° W 63. 135° ; S 45° E 65. 220 mi 67. 47 nautical mi 69. 2203 ft 71. 148 mi 73. 430 mi 75. 140 mi 77. 114 ft 79. 5.18 m 81. 433 ft 83. 10.8 ft 85. 1.95 mi 87. (a) d = b 2 Acot a 2 + cot b 2B (b) 345.4 cm 89. (a) 320 ft (b) R A1 - cos u 2B Chapter 5 Review Exercises 1. complement: 55°; supplement: 145° 3. 186° 5. 9360° 7. 119.134° 9. 275° 06′ 02″ In Exercises 11–35, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 11. - 23 2 ; 1 2 ; - 23; - 23 3 ; 2; - 223 3 13. 0; -1; 0; undefined; -1; undefined 15. - 4 5 ; 3 5 ; - 4 3 ; - 3 4 ; 5 3 ; - 5 4 17. 15 17 ; - 8 17 ; - 15 8 ; - 8 15 ; - 17 8 ; 17 15 19. 22 2 ; - 22 2 ; -1; -1; - 22; 22 21. 0 x y (3, 5) 3 5 5x – 3y = 0, x ≥ 0 U 5234 34 ; 3234 34 ; 5 3 ; 3 5 ; 234 3 ; 234 5 23. 0; -1; 0; undefined; -1; undefined 25. - 239 8 ; - 5 8 ; 239 5 ; 5239 39 ; - 8 5 ; - 8239 39 27. 2 25 5 ; - 25 5 ; -2; - 1 2 ; - 25 ; 25 2 29. - 3 5 ; 4 5 ; - 3 4 ; - 4 3 ; 5 4 ; - 5 3
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