Amplitude and Period of Sine and Cosine Functions

The amplitude of y=asin( x ) and y=acos( 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=asin( bx ) and y=acos( bx ) is given by

Period= 2π | 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=acos( bx ) to find a and b .

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

The amplitude of the function is 5 2 .

Period= 2π | 0.25 | =8π

The period of the function is 8π .