A-30 Answers to Selected Exercises 15. 0 x y (–8, 15) 15 –5 –15 U 15 17 ; - 8 17 ; - 15 8 ; - 8 15 ; - 17 8 ; 17 15 17. 0 x y (–7, –24) –30 –20 –10 U –30 –20 –10 10 - 24 25 ; - 7 25 ; 24 7 ; 7 24 ; - 25 7 ; - 25 24 19. 0 x y (0, 2) 2 –2 –2 U 2 1; 0; undefined; 0; undefined; 1 21. 0 x y (–4, 0) 4 –4 U 4 0; -1; 0; undefined; -1; undefined 23. 0 x y –1 1 –1 U 1 (1, Ë3) 23 2 ; 1 2 ; 23; 23 3 ; 2; 223 3 25. 0 x y –3 3 –3 U 3 (–2Ë3, –2) - 1 2 ; - 23 2 ; 23 3 ; 23; - 2 23 3 ; -2 27. negative 29. negative 31. positive 33. positive 35. negative 37. positive 39. negative 41. positive 43. 0 x y (1, –2) 1 –2 2x + y = 0, x ≥ 0 U - 2 25 5 ; 25 5 ; -2; - 1 2 ; 25; - 25 2 45. 0 x y (–7, –4) –7 –4 –4x + 7y = 0, x ≤ 0 U - 4 265 65 ; - 7265 65 ; 4 7 ; 7 4 ; - 265 7 ; - 265 4 47. 0 x y (2, –2) –2 2 x + y = 0, x ≥ 0 U 2 –2 - 22 2 ; 22 2 ; -1; -1; 2; -22 49. 0 x y –2 2 U 2 –2 –Ë3x + y = 0, x ≤ 0 (–1, –Ë3) - 23 2 ; - 1 2 ; 23; 23 3 ; -2; - 223 3 109. I, II 111. I 113. II 115. I 117. III 119. III, IV 121. impossible 123. possible 125. possible 127. impossible 129. possible 131. - 4 5 133. - 25 2 135. - 23 3 137. 1.05 In Exercises 139–149, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 139. 15 17 ; - 8 17 ; - 15 8 ; - 8 15 ; - 17 8 ; 17 15 141. 25 7 ; 2211 7 ; 255 22 ; 2255 5 ; 7211 22 ; 725 5 143. 8 267 67 ; 2201 67 ; 823 3 ; 23 8 ; 2201 3 ; 267 8 145. 22 6 ; - 234 6 ; - 217 17 ; - 217 ; - 3 234 17 ; 3 22 147. 215 4 ; - 1 4 ; - 215; - 215 15 ; -4; 4215 15 149. 1; 0; undefined; 0; undefined; 1 153. negative 155. positive 157. positive 159. positive 5.3 Exercises 1. C 3. B 5. E 7. negative; III; 60°; - 23 2 9. positive; III; 30°; 23 3 In Exercises 11 and 13, we give, in order, sine, cosine, and tangent. 11. 21 29 ; 20 29 ; 21 20 13. n p ; m p ; n m In Exercises 15–21, we give, in order, the unknown side, sine, cosine, tangent, cotangent, secant, and cosecant. 15. c = 13; 12 13 ; 5 13 ; 12 5 ; 5 12 ; 13 5 ; 13 12 17. b = 213 ; 213 7 ; 6 7 ; 213 6 ; 6213 13 ; 7 6 ; 7213 13 19. b = 291 ; 291 10 ; 3 10 ; 291 3 ; 3291 91 ; 10 3 ; 10291 91 21. b = 23 ; 23 2 ; 1 2 ; 23 ; 23 3 ; 2; 223 3 23. sin 60° 25. sec 30° 27. csc 51° 29. cos 51.3° 31. 23 3 33. 1 2 35. 223 3 37. 22 39. 22 2 41. 1 43. 23 2 45. 23 47. y = 23 3 x 49. 60° 51. x = 9 23 2 ; y = 9 2 ; z = 323 2 ; w = 3 23 53. p = 15 ; r = 1522 ; q = 526 ; t = 1026 55. = s 2 2 57. C 59. A 61. D 63. 23 3 ; 23 65. 23 2 ; 23 3 ; 223 3 67. -1; -1 69. - 23 2 ; - 223 3 In Exercises 71–87, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 71. - 23 2 ; 1 2 ; - 23 ; - 23 3 ; 2; - 223 3 73. 22 2 ; 22 2 ; 1; 1; 22 ; 22 75. 23 2 ; - 1 2 ; - 23 ; - 23 3 ; -2; 223 3 77. - 1 2 ; - 23 2 ; 23 3 ; 23 ; - 2 23 3 ; -2 51. 0 53. 0 55. -1 57. 1 59. undefined 61. -1 63. 0 65. undefined 67. 1 69. -1 71. -3 73. -3 75. 5 77. 0 79. 1 81. 0 83. 0 85. undefined 87. 3 2 89. - 7 3 91. 1 5 93. 22 2 95. 0.8 97. All are positive. 99. Tangent and cotangent are positive. All others are negative. 101. Sine and cosecant are positive. All others are negative. 103. Cosine and secant are positive. All others are negative. 105. Sine and cosecant are positive. All others are negative. 107. All are positive.
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