PHS_Algebra_2_Chapter_13 4/7/06 9:33 AM Page 324
Answers for Lesson 13-4
Exercises
1. 12
2. <0.7
3. <0.9
4. 0
5. <-0.9
6. <-0.9
7. 1
8. <0.1
9. <-0.8
10. <-1
11. -1
12. <-0.7
13. 3; 2, 2p
3
14. 12; 1, 4p
15. 2; 3, p
16.
1
y
17.
2π
3
π
3
O
y
3π
4
π
4
O
π
32
y = 2 sin 3u
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2
3
y = 13 sin 2u
18.
19.
y
2
O
2
π
3π
2
y
2π
π
O
2
y = 4 sin 12u
y = 3 sin u
20.
21.
y
0.5
1
y
O
O 0.5
1
y = 1.5 sin 2p
3u
y = sin pu
22.
1
23.
y
O
π
2
3π
2
1 y
25.
1 y
Algebra 2
y
2
O
1
2π
3
π
3
O
1
24.
2
O
4
2
Chapter 13
324
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Answers for Lesson 13-4
26.
Exercises (cont.)
27.
y
2
y
2
4π
O
2π
O
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2
4π
2
28. 2p; y = 2 sin u
29. 2p; y = -3 sin u
30. p; y = 25 sin 2u
31. p3 ; y = 21 sin 6u
32. p; y = -sin 2u
33. 4; y = 3 sin p2 u
34. 1; 1, 2p
35. 5; 1, 2p
5
36. p; 1, 2
37. 1; 3, 2p
38. 1; 5, 2p
39. 2p; 5, 1
40. a.
b. As a increases, the amplitude of the graph increases.
41. a.
They are reflections of each other in the x-axis.
b.
They are reflections of each other in the x-axis.
c. When either a or b is replaced by its opposite, the graph
is a reflection of the original graph in the x-axis.
Algebra 2
Chapter 13
325
PHS_Algebra_2_Chapter_13 4/7/06 9:33 AM Page 326
Answers for Lesson 13-4
Exercises (cont.)
42. a. p
b. 4
1
43. a. 440
b. 0.001
c. 880p
44. • ∆a∆ is the amplitude of the function.
• b is the number of cycles in the interval 08 to 3608.
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• 3608
is the period of the function. The properties relating
b
to number of cycles and period are affected.
45. 2p
5 , 3.5
46. p, 52
4 y
y
2
2
π
O
O
π
4
5π
4
2
2
4
48. 2p
3 , 0.4
47. 1, 2
2
y
0.5
7
O
2
y
2π
¨
π
O
0.5
50. 12
5 , 1.2
49. 6, 0.5
0.5
O
y
1.2
2
4
0.5
y
O 0.6 1.8
3
4.2
5.4 1.2
51. Check students’ work.
Algebra 2
Chapter 13
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Answers for Lesson 13-4
Exercises (cont.)
52. a. 4, 2p
b. y = 4 sin u
c. coil B
53. y = sin 60pu
54. y = sin 30pu
55. y = sin 240,000pu
56. 2p, 1
1
y
O
1
3
5
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1
57. 2p, 1
1
58. p, 1
y
1
O
2
4
O
2
6
1
y
5
1
59. a. days from spring equinox, hours of sunlight
b. 23
h, about 365 days
12
2px
c. y = 23
sin
365
12
d. 1.1 h
e. Check students’ work.
Algebra 2
Chapter 13
327