Graphing Sine and Cosine Functions
Explore and graph sine and cosine functions, analyzing amplitude, period, phase shift, and vertical shift for Grade 11 mathematics.
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Graphing Sine and Cosine Functions
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Read each question carefully and follow the instructions. Show all your work for full credit. Use the provided graph paper for sketching graphs. Remember the general forms: y = A sin(Bx - C) + D and y = A cos(Bx - C) + D.
1. For the function y = 3sin(2x + π) - 1, identify the amplitude, period, phase shift, and vertical shift.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
2. Graph one full period of the function y = 2sin(x - π/2). Clearly label the amplitude, period, phase shift, and key points on your graph.
3. The of a sinusoidal function is half the distance between its maximum and minimum values.
4. A positive phase shift moves the graph to the .
5. Graph one full period of the function y = -cos(2x) + 3. Label the amplitude, period, phase shift, vertical shift, and key points.
6. The period of y = sin(x/2) is π.
True
False
7. A vertical shift of +2 moves the midline of the graph up by 2 units.
True
False
8. Write the equation of a sine function with an amplitude of 4, a period of π, a phase shift of π/4 to the left, and a vertical shift of -2.
9. Which of the following functions has an amplitude of 0.5 and a period of 4π?
y = 0.5 sin(2x)
y = 0.5 cos(x/2)
y = 2 sin(0.5x)
y = 2 cos(x/4)
The image below illustrates a basic sinusoidal wave.
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