Grade 11 Sine and Cosine Graphs Worksheet
Explore the properties and transformations of sine and cosine functions through graphing, amplitude, period, phase shift, and vertical shift.
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Grade 11 Sine and Cosine Graphs
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Date:
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Read each question carefully and answer to the best of your ability. Show all work where applicable.
1. What is the amplitude of the function y = 3sin(2x - π) + 1?
1
2
3
π
2. Which of the following functions has a period of π?
y = sin(x)
y = cos(2x)
y = sin(x/2)
y = cos(4x)
1. The of a sinusoidal function is half the distance between its maximum and minimum values.
2. A horizontal shift of a trigonometric graph is called a .
3. The equation of the midline for y = A sin(Bx + C) + D is y = .
1. Describe the effect of changing the value of 'B' in the function y = A sin(Bx - C) + D on its graph.
1. Graph one full period of the function y = 2cos(x + π/2) - 1 on the coordinate plane below. Label the amplitude, period, phase shift, and vertical shift.
1. The graph of y = sin(x) passes through the origin (0,0).
True
False
2. A phase shift to the right is indicated by a positive value of 'C' in the expression (Bx - C).
True
False
Match the transformation type with its corresponding parameter in y = A sin(Bx - C) + D.
1. Amplitude
a. B
2. Period
b. C
3. Phase Shift
c. A
4. Vertical Shift
d. D
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