NAME
DATE
4-5
PERIOD
Practice
Graphing Other Trigonometric Functions
Locate the vertical asymptotes, and sketch the graph of each function.
π
2. y = −2 cot 2x + −
(
1. y = −3 tan x
y
)
3
y
2
2
0
-2π -π
π
2π
x
-2π
-π 0
x
-2
-2
x
4. y = sec −
+π –1
(3
3. y = csc x + 3
-1 0
-2
)
y
y
8
7
6
5
4
3
2
-3π
2
2π
π
4
3
2
1
-3
-4
θ
3π
2
3π θ
-1 0
-3π
1
x cos 2x
5. y = −
2
1
f(x) = −
x;
2
πx
3
6. y = − −
x sin −
2
the amplitude of the function is
decreasing as x approaches 0
[-3π, 3π] scl:
2
3
f(x) = − −
x;
2
the amplitude of the function is
decreasing as x approaches 0
[-3π, 3π] scl:
π
by [-10, 10] scl: 1
2
π
by [-10, 10] scl: 1
2
7. MUSIC A guitar string is plucked at a distance of 0.6 centimeter above its resting
position and then released, causing vibration. The damping constant of the guitar
string is 1.8, and the note produced has a frequency of 105 cycles per second.
a. Write a trigonometric function that models the motion of the string.
y = 0.6e -1.8t cos 210πt
b. Determine the amount of time t that it takes the string to be damped so that
-0.24≤ y ≤ 0.24. 0.5 s
Chapter 4
28
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Identify the damping factor f(x) of the function. Then use a graphing calculator
to sketch the graphs of f(x), −f(x), and the given function in the same viewing
window. Describe the behavior of the graph.