AN48 Answers: Chapter 6 51. 9 2 , 10 3 2 , 22 9 2 , 22 2 3 2 , 10 2 y 10 210 x (23, 4) (0, 4) (3, 4) (6, 4) 10 210 Domain: , ( ) −∞∞ Range: 2, 10 [ ] − 53. P 4 , 2 P 2 , 5 P 4 , 8 2 P 2 , 5 2 3P 4 , 2 2 3P 4 , 8 y 22 8 x (0, 5) 2P P (P, 5) (2P, 5) Domain: , ( ) −∞∞ Range: 2, 8 [ ] 55. 3 2 , 0 9 4 5 3 , 3 4 5 3 , 2 9 4 , 2 5 3 2 3 4 , 2 5 3 y 2.5 22.5 x (3, 0) (0, 0) 5 25 Domain: , ( ) −∞∞ ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ Range: 5 3 , 5 3 57. 26, 1 2 1 2 2, 1 2 6, (28, 21) y 2.5 22.5 x 10 (8, 21) (24, 2) (0, 21) (4, 2) ( ) −∞∞ Domain: , [ ] − Range: 1, 2 101. A BC A k B C k 0, cos , 2 1 , 0 , is an integer π ( ) ( ) ( ) ( ) − + + + 107. x h 2 5 + − 108. 2, 5 ( ) 109. 0, 5 , ( ) 5 3 , 0 , 7 3 , 0 ( ) ( ) − − 110. 8 { } − 111. 17.4 years 112. ln7 3 0.649 { } ≈ 113. y x2 7 = + 114. 19 12 , ) ⎡ − ∞ ⎣ ⎢ 115. , 2 4 3 , ( ) ( ] −∞ − ∪ ∞ 116. 1 10 { } + 6.5 Assess Your Understanding (page 448) 3. (a) , ( ) −∞∞ (b) odd; origin (c) π (d) odd; 2 π (e) 1, 1, 0 − 4. y-axis; odd multiples of 2 π 5. b 6. T 7. 0 9. 1 11. x sec 1 = for x x 2 , 0, 2 ; sec 1 π π = − = − for x , π π = − 13. 3 2 , 2 , 2 , 3 2 π π π π − − 15. 3 2 , 2 , 2 , 3 2 π π π π − − 81. ( )( ) ( ) = f g x x sin 4 , 0 P 2 2 P 2 , 0 y 1.25 x 2P ( )( ) = g f x x 4 sin P 2 , 4 3P 2 , 24 y 5 25 x 2P 22P 83. ( )( ) = − f g x x 2 cos (0, 22) (2P, 22) (P, 2) y 2.25 x 2P ( )( ) ( ) = − g f x x cos 2 (P, 1) y 1.25 x P P 2 , 21 85. Ï2 y x 1.25 2p (2p, 1) (0, 0) (p, 0) p 2 , 1 3p 2 , 0 5p 4 2 , 2 87. y 1.25 x 2P 89. = Period 1 30 sec = Amplitude 220 amp I 220 t 2220 1 15 91. (a) P t V ft R V R ft sin 2 sin 2 0 2 0 2 2 π π [ ] ( ) ( ) ( ) = = (b) Since the graph of P has amplitude V R2 0 2 and period f 1 2 and is of the form y A t B cos , ω( ) = + then A V R2 0 2 = − and B V R2 . 0 2 = Since f 1 2 2 , π ω = then f 4 . ω π = Therefore, P t V R ft V R V R ft 2 cos 4 2 2 1 cos 4 . 0 2 0 2 0 2 π π ( ) ( ) [ ] ( ) = − + = − 93. (a) 120 (b) 80 (c) 70 beats per minute 95. (a) 75.4 F° (b) 28.1 F° (c) 6 months 97. (a) 205 ft (b) 5 ft (c) 3 (d) 4.3 mihr 99. (a) Physical potential: 2 23 ; ω π = emotional potential: 14 ; ω π = intellectual potential: 2 33 ω π = (b) 0 0 100 36 (c) No1 (d) Physical potential peaks at 15 days after 20th birthday. Emotional potential is 50% at 17 days, with a maximum at 10 days and a minimum at 24 days. Intellectual potential starts fairly high, drops to a minimum at 13 days, and rises to a maximum at 29 days. 17. y x P 4 2 , 23 P 4 , 3 2P 6 x x k k Domain: 2 , is an odd integer π { } ≠ Range: , ( ) −∞∞ 19. y 16 x 2P P 4 2 , 24 P 4 , 4 x x k k Domain: , is an integer π { } ≠ Range: , ( ) −∞∞ 21. y x 1 2 , 1 1 2 2 , 21 4 5 x x Domain: does not equal an odd integer { } Range: , ( ) −∞∞ 23. (P, 1) (2P, 21) y 5 x 4P x x k k Domain: 4 , is an integer π { } ≠ Range: , ( ) −∞∞ 25. (2P, 2) (0, 2) (P, 22) (2P, 22) y x 2P 1 x x k k Domain: 2 , is an odd integer π { } ≠ y y y Range: 2 or 2 { } ≤− ≥ 27. y x P 2 , 23 3P 2 , 23 2 3P 2 , 3 P 2 , 3 2 15 2P x x k k Domain: , is an integer π { } ≠ y y y Range: 3 or 3 { } ≤− ≥ 59. ( ) = ± y x 3 sin 2 61. π( ) = ± y x 3 sin 63. π( ) = y x 5 cos 4 65. ( ) = − y x 3 cos 1 2 67. π ( ) = y x 3 4 sin 2 69. ( ) = − y x sin 3 2 71. π ( ) = − + y x cos 4 3 1 73. π( ) = y x 3 sin 2 75. ( ) = − y x 4 cos 3 77. π 2 79. π 2
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