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Precalculus HW
Name ______________________
4.5 Graphing Sine and Cosine Functions Review Worksheet
Identify the amplitude, period, and phase shift of the given function.
1.
y = 3cos ⎛⎜ x +
⎝
π ⎞
⎟ + 1
2.
4 ⎠
y = 5 sin ⎛⎜ 2x −
⎝
π ⎞
⎟
3 ⎠
Write the indicated function of each graph.
3.
4.
Sine: ____________________________________
Cosine: ___________________________________
Write the equation of a function with the given characteristics.
5.
Cosine Function
Amplitude = 2
Period =
6.
π
3
Sine Function
Amplitude = 3
Period = 8π
Phase Shift =
Vertical shift = 1
π
2
Reflection in the x-axis
Match the function to its graph.
7.
A.
y = 2sin (2x )
8.
B.
y = 2 − sin (2x )
9.
C.
y = −2sin x
Graph each of the functions. Include all relative extrema and intercepts. Graph as many periods of the
function that will fit on the grid provided. List the amplitude, period, phase shift, and vertical shift for
each function.
10.
y = − sin ⎛⎜ x −
⎝
π ⎞
⎟
4 ⎠
11. y = 2cos
1
x
4
1
1
π
π
2
Amp: _____ Per: ______ PS: ______ VS:
Amp: _____ Per: ______ PS: ______ VS: ______
______
12.
y = −3cos (x − π ) + 4
13.
y = cos ⎛⎜ x +
⎝
π ⎞
⎟ + 1
3 ⎠
1
π
2
1
π
2
Amp: _____ Per: ______ PS: ______ VS: ______
14.
y = −1 + 3sin (x + π )
Amp: _____ Per: ______ PS: ______ VS: ______
15.
1
⎛
⎝
y = 3sin ⎜ x −
⎞
⎟ − 2
⎠
1
π
π
2
2
Amp: _____ Per: ______ PS: ______ VS: ______
16.
3π
2
⎛ 1
⎝ 2
⎞
⎠
y = − cos ⎜ x ⎟ − 2
1
Amp: _____ Per: ______ PS: ______ VS: ______
17.
y = −2cos ⎛⎜ x +
⎝
1
π
2
π
2
π ⎞
⎟
6 ⎠
Amp: _____ Per: ______ PS: ______ VS: ______
Amp: _____ Per: ______ PS: ______ VS: ______

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