Trigonometric Graphs Worksheet
Explore and analyze the graphs of sine, cosine, and tangent functions, including their amplitude, period, phase shift, and vertical shift.
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Trigonometric Graphs Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. What is the amplitude of the function y = 3sin(2x) + 1?
1
2
3
4
2. The period of the function y = cos(x/2) is:
π
2π
3π
4π
3. The graph of y = tan(x) has vertical asymptotes at odd multiples of .
4. A phase shift of a trigonometric function moves the graph horizontally, while a vertical shift moves it .
5. Describe how the graph of y = sin(x) changes when transformed into y = -2sin(x - π/4).
6. The range of y = cos(x) is [-1, 1].
True
False
7. The period of y = tan(x) is 2π.
True
False
8. Graph one full period of the function y = 2cos(x) - 1 on the coordinate plane below.
Match the trigonometric function characteristic with its definition.
9. Amplitude
a. The horizontal shift of the graph
10. Period
b. Half the distance between the maximum and minimum values
11. Phase Shift
c. The length of one complete cycle of the graph