# How do you find the amplitude and period of a function y=cos²(x)?

Dec 7, 2015

First, simply graph each function ... the blue line is the new function and the red line is cos x .

#### Explanation:

Since this function is squared, it must always be positive. Also, since cos x fluctuates between -1 and 1, then squaring it, the new function will fluctuate between 0 and 1.

The period will also be cut in half .

amplitude $= \frac{1}{2} \left(0 + 1\right) = \frac{1}{2}$

period $= \pi$

hope that helped