NAME
DATE
4-4
PERIOD
Practice
Graphing Sine and Cosine Functions
Describe how the graphs of f(x) and g(x) are related. Then find the amplitude
of g(x) and sketch two periods of both functions on the same coordinate axes.
1. f(x) = sin x
2. f(x) = cos x
1
sin x
g(x) = −
1
cos x
g(x) = - −
The graph of g(x) is the graph of
f(x) compressed vertically. The
1
.
amplitude of g(x) is −
The graph of g(x) is the graph of
f(x) compressed vertically and
reflected in the x-axis. The
1
.
amplitude of g(x) is −
3
4
3
1
y
3
0
-1
2π
π
4
g (x) = 1 sin x
f (x ) = sin x
1
0
x
4π
g (x ) = - 1 cos x
y f (x) = cos x
2π
π
-1
4
3π
4π
x
State the amplitude, period, frequency, phase shift, and vertical shift of each
function. Then graph two periods of the function.
π
-3
3. y = 2 sin x + −
(
2
1
4. y = −
cos (2x − π) + 2
)
2
amplitude = 2; period = 2π;
1
amplitude = −
; period = π;
1
frequency = −
;
2π π
phase shift = − −;
2
vertical shift = 2
2
π
1
frequency = −
;
π ; phase shift = −
2
y
y
4
4
2
-2π
2
2π
π
-π
x
0
-π
0
-π
2
-2
-4
π
2
π
x
-4
Write a sinusoidal function with the given amplitude, period, phase shift, and
vertical shift.
π
, vertical shift = -10
5. sine function: amplitude = 15, period = 4π, phase shift = −
(
2
)
π
x
y = ±15 sin −
-−
- 10
2
4
π
π
2
6. cosine function: amplitude = −
, period = −
, phase shift = - −
, vertical shift = 5
3
3
3
2
y=±−
cos (6x + 2π) + 5
3
7. MUSIC A piano tuner strikes a tuning fork note A above middle C and sets in motion
vibrations that can be modeled by y = 0.001 sin 880tπ. Find the amplitude and period of
the function.
Chapter 4
1
0.001; −
440
22
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
vertical shift = −3