Section 6.2 AN45 Cumulative Review (page 380) 1. Yes; no 2. (a) 10 (b) x x 2 3 1 2 + + (c) x xh h x h 2 4 2 3 3 1 2 2 + + − − + 3. 1 2 , 3 2 ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ is on the graph. 4. 26 { } − 5. y x 10 10 (8, 0) (0, 24) 6. (a) y x 10 10 (1, 22) (0, 23) (b) x x { } −∞< <∞ 7. f x x x x 2 4 8 2 16 24 2 2 ( ) ( ) = − − = − + 8. y x 10 5 (0, 1) (21, 22) 9. f g x x 4 3 2; 2 ( ) ( ) ( ) = − + domain: x x 3 ; 3 { } ≠ 10. (a) y x3 4 = (b) x-intercepts: 2, 0, 2, 5; − y-intercept: 0 (c) 2, 0, 2, 5: − multiplicity 1, crosses (d) At most 3 turning points (e) x y 700 (23, 360) (2, 0) (1, 36) (6, 576) (0, 0) (22, 0) (21, 254) (3, 290) (4, 2144) (5, 0) 2300 7 11. (a), (c) y x 5 5 (0, 3) (3, 0) g21(x) g(x) y 5 2 x 5 2 y 5 x Domain g g range , 1 ( ) = = −∞ ∞ − Range g g domain 2, 1 ( ) = = ∞ − (b) g x x log 2 1 3 ( ) ( ) = − − 12. { } − 3 2 13. 2{ } 14. (a) 1 { } − (b) x x 1 { } >− or 1, ( ) − ∞ (c) 25 { } 15. (a) 0 20 0 80 (b) Logarithmic; y x 49.293 10.563 ln = − (c) Highest value of r CHAPTER 6 Trigonometric Functions 6.1 Assess Your Understanding (page 392) 3. standard position 4. central angle 5. d 6. θ θ r r ; 1 2 2 7. b 8. θ s t t ; 9. T 10. F 11. 308 13. 1358 15. 4508 17. 3p 4 19. –p 6 21. 16p 3 23. π 6 25. π 11 4 27. π − 3 29. π3 31. π − 4 3 33. π − 2 35. ° 60 37. − ° 390 39. ° 810 41. ° 27 43. − ° 90 45. − ° 204 47. 0.30 49. −0.70 51. 2.18 53. ° 179.91 55. ° 401.07 57. ° 531.70 59. ° 40.17 61. ° 50.24 63. ° 9.15 65. ° ′ ′′ 40 19 12 67. ° ′ ′′ 18 15 18 69. ° ′ ′′ 19 59 24 71. 5 m 73. 12 ft 75. 0.9 radian 77. π ≈ 3 1.047 in. 79. 25 m2 81. ≈ 2 3 3.464 ft 83. 0.24 radian 85. π ≈ 3 1.047 in.2 87. = = s A 2.094 ft; 2.094 ft2 89. = = s A 14.661 yd; 87.965 yd2 91. π π ≈ ≈ 3 9.42 in; 5 15.71 in. 93. π ≈ 2 6.28 m2 95. π ≈ 675 2 1060.29 ft2 97. π ≈ 1075 3 1125.74 in.2 99. ω = = v 1 60 radian sec; 1 12 cm sec 101. ≈23.2 mi hr 103. ≈585.8 km hr 105. ≈452.5 rpm 107. 61.54 ft 109. ≈898 mi hr 111. ≈2292 mi hr 113. 3 4 rpm 115. ≈2.86 mi hr 117. ≈31.47 rpm 119. ≈1037 mihr 121. ≈ ≈ Radius 3979 mi; circumference 25,000 mi 123. π 63 ft2 125. ≈2.2 rev 133. = − x 7 3 134. { } −3, 1 5 135. = − + − y x 3 4 136. = = y x HA: 3; VA: 7 137. = c 5 2 138. { } 21 4 139. { } ≠ − ≠ x x x 3, 3 140. + + x xh h 6 6 2 2 2 141. − + − x x x 27 54 36 8 3 2 142. (a) ( ) −3, 395.65 ; ( ) − 1, 39.55; ( ) 4, 69.8 ; ( ) − 7, 104.35 2300 25 9 500 (b) −3, 1, 4, 7 (c) The values are the same. (d) ( ] [ ] [ ) −∞ − ∞ , 3, 1,4, 7, (e) ( ] [ ] [ ) −∞ − ∞ , 3, 1,4, 7, (f) The intervals are the same. 6.2 Assess Your Understanding (page 408) 7. b 8. ( ) 0, 1 9. ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 2 2 , 2 2 10. F 11. y r x r ; 12. a 13. = = = = = = t t t t t t sin 1 2 ; cos 3 2 ; tan 3 3 ; csc 2; sec 2 3 3 ; cot 3 15. = = − = − = = − t t t t t sin 21 5 ; cos 2 5 ; tan 21 2 ; csc 5 21 21 ; sec 5 2 ; = − t cot 2 21 21 17. = = − t t sin 2 2 ; cos 2 2 ; = − = = − = − t t t t tan 1; csc 2; sec 2; cot 1 19. = − = = − = − = = − t t t t t t sin 1 3 ; cos 2 2 3 ; tan 2 4 ; csc 3; sec 3 2 4 ; cot 2 2
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