Write Cosine Function Given Maximum and Minimum

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Question Description

Write a cosine function, f(x), such that on one period a local maximum is at (-pi/3, 1) followed by a local mnimum at (2pi/3, -7).  

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Explanation & Answer

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Since the difference between maximum and minimum is 8, the amplitude is 4.

Since the local maximum is at -pi/3, you add pi/3 to the x value.

Since the difference in the x value of the maximum and minimum is pi, the period is 2pi.

Since the average between the maximum and minimum is -3, you add 3 to the y value.

This leaves you with the equation y = 4cos(x+pi/3) - 3

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Wbanguna U. (87)
University of Maryland

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