NAME DATE PERIOD 4-5 Practice - SD308

NAME

DATE

PERIOD

4-5 Practice

Graphing Other Trigonometric Functions

Locate the vertical asymptotes, and sketch the graph of each function.

1. y = -3 tan x

y 2

( ) 2. y = -2 cot 2x + -3

y

2

-2 - 0 2 x -2

-2 - 0 -2

2 x

3. y = csc x + 3

y 8 7 6 5 4 3 2

-3

-1 0

2

-2

3 2

( ) 4. y = sec -3x + ? 1

y

4 3 2 1

-3

-1 0

-3 -4

3

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.

5. y = -12 x cos 2x f(x) = -12 x; the amplitude of the function is

decreasing as x approaches 0

6. y = - -32 x sin - 2x f(x) = - -32 x; the amplitude of the function is

decreasing as x approaches 0

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

[-3, 3] scl:

2

by

[-10,

10]

scl:

1

[-3, 3] scl:

2

by

[-10,

10]

scl:

1

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 210t

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

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