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326 Chapter 4 Trigonometry
4.5 EXERCISES
See www.CalcChat.com for worked-out solutions to odd-numbered exercises.
VOCABULARY: Fill in the blanks.
1. One period of a sine or cosine function is called one ________ of the sine or cosine curve.
2. The ________ of a sine or cosine curve represents half the distance between the maximum and minimum values
of the function.
c
3. For the function given by y a sinbx c, represents the ________ ________ of the graph of the function.
b
4. For the function given by y d a cosbx c, d represents a ________ ________ of the graph of the function.
SKILLS AND APPLICATIONS
In Exercises 5–18, find the period and amplitude.
5. y 2 sin 5x
6. y 3 cos 2x
3
2
1
−3
1
−1
1
−1
y
y
y
π
10
π 2π
9. y 1 10. y 3 2 sin x
3
2 cos
π
2
11. y 4 sin x 12.
y
13. y 3 sin 10x 14. y 1 5 sin 6x
15. y 5 4x
cos
3 5
16. y 5 2 cos x 4
17. 18. y 2 3 cos x
y 1 sin 2x
4 10
x
x
x
−π
−2
−3
7. y 3 8. y 3 sin x 4 cos x 2
3
4
−π
−2
−4
2
−2
y
y
y
π
cos 2x
3
π
2
x
2
π
x
x
x
In Exercises 19–26, describe the relationship between the
graphs of f and g. Consider amplitude, period, and shifts.
19. f x sin x
20. f x cos x
gx sinx gx cosx
21. f x cos 2x 22. f x sin 3x
gx cos 2x
gx sin3x
23. f x cos x
24. f x sin x
gx cos 2x
gx sin 3x
25. f x sin 2x 26. f x cos 4x
gx 3 sin 2x gx 2 cos 4x
In Exercises 27–30, describe the relationship between the
graphs of f and g. Consider amplitude, period, and shifts.
27. 28.
29. 30.
−2π
3
−2
−3
3
2
1
−2
−3
y
y
2π
In Exercises 31–38, graph f and g on the same set of
coordinate axes. (Include two full periods.)
31. f x 2 sin x 32. f x sin x
gx 4 sin x
f
f
π
g
g
x
x
−2π
gx sin x 3
2π
33. f x cos x
34. f x 2 cos 2x
gx 2 cos x gx cos 4x
g
3
2
−2
−3
4
3
2
−2
y
y
g
f
f
π
x
x