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f(x) = a*cos(bx + c) + d
in blue and
f(x) = a*cos(bx) + d
in red as shown in the figure below. This is to explain the effects of c on the phase shift.
You may also want to consider another tutorial on the trigonometric unit circle .
Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs .
Interactive Tutorial
Click on the button above "click here to start" and maximize the window obtained.
Explore how the 4 coefficients a,b,c and d affect the graph of f(x)?
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Use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the amplitude, period and phase shift of f(x)? Now change a , how does it affect the graph?
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Set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)?
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set a=1,b=1,d=0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to
-c/b.
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set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to
-c/b.
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repeat 3 and 4 above for b=2,3 and 4.
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set a,b and c to non zero values and change d. What is the direction of the shift of the graph when d is positive and when d is negative?
Links to topics related to cosine function
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