Chapter 10 - NCPN

Practice and Problem Solving
Identify the amplitude, period, and number of cycles in the
interval from 0 to 2π for each trigonometric function. (Assume
that θ is given in radians.)
6. y = 1.5sin 2θ 7. y = 4cos θ
8. y = –2sin θ 9. y = 3cos θ 2
10. y = 0.2cos 0.2θ 11. y = –1.5sin θ 3
12. y = 3sin (θ + π) 13. y = cos ( θ − π )
1 2 2 2
Identify the period and the location of two vertical asymptotes
for each function. (Assume that θ is given in radians.)
14. y = tan 2θ 15. y = 3tan θ
1
2
1
3
16. y = 7.5tan θ 2
17. y = 2tan (θ + π)
Graph each trigonometric function over the specified domain.
18. y = 2cos 2θ, 0 ≤ θ ≤ 2π 19. y = sin 2θ, 0 ≤ θ ≤ 360°
20. y = tan 2θ, –180° ≤ θ ≤ 180° 21. y = 2cos θ, –2π ≤ θ ≤ 2π
22. y = tan ≠ θ, –4.5 ≤ θ ≤ 4.5 23. y = –1.5sin θ, –2π ≤ θ ≤ 2π
3
24. Sounds traveling through the air can be modeled by sine waves.
The sound of a car horn can be represented by the function
y = 8sin 160θ.
a. The loudness of a sound is related to the
amplitude of its sound wave. Write a new
function for a sound that is twice as loud as
the car horn.
b. Sounds are caused by vibrations. When an
object vibrates twice as fast, it produces
a sound with a pitch that is one octave
higher. The period of the sound wave is half
the original period. Write a new function
for a sound that is the same loudness as
the car horn, but one octave higher.
c. Graph the function modeling the sound of the car horn over
the interval 0 ≤ θ ≤ 0.1.
460 Chapter 10 Trigonometric Functions and Identities