Sine and Cosine Graphs Worksheet
Explore the properties of sine and cosine functions through graphing, identifying key features like amplitude, period, and phase shift.
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Sine and Cosine Graphs
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Read each question carefully and provide detailed answers or complete the graphs as instructed.
1. What is the amplitude of the function y = 3sin(2x)?
2. What is the period of the function y = cos(x/3)?
3. Identify the phase shift of the function y = sin(x - π/4).
4. Which of the following functions has an amplitude of 2 and a period of π?
y = 2sin(x)
y = sin(2x)
y = 2sin(2x)
y = 2cos(x/2)
5. What is the range of the function y = 4cos(x) - 1?
[-4, 4]
[-5, 3]
[-1, 1]
[-3, 5]
6. Graph one full period of the function y = 2sin(x). Label the axes and key points (maxima, minima, and intercepts).
7. Graph one full period of the function y = cos(x) + 1. Label the axes and key points.
8. The of a sinusoidal function is half the distance between its maximum and minimum values.
9. The of y = sin(Bx) is given by the formula 2π/|B|.
10. A shift moves the entire graph horizontally.
11. The graph of y = sin(x) passes through the origin (0,0).
True
False
12. The maximum value of y = cos(x) is 1.
True
False
13. Consider the following wave graph:
a) What is the amplitude of this wave?
b) If the wave completes one cycle in 4 seconds, what is its period?