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Amplitude and Period of Sine and Cosine Functions

The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function.

Amplitude = | a |

Let b be a real number. The period of y = a sin ( b x ) and y = a cos ( b x ) is given by

Period = 2 π | b |

Example:

Find the period and amplitude of y = 5 2 cos ( x 4 ) .

Solution:

Compare the functions y = 5 2 cos ( x 4 ) and y = a cos ( b x ) to find a and b .

Amplitude = | a | = | 5 2 | = 5 2

The amplitude of the function is 5 2 .

Period = 2 π | 0.25 | = 8 π

The period of the function is 8 π .

 

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