# What is the graph of y=cos^2 x?

Mar 22, 2015

Here is the graph:
graph{y=(cosx)^2 [-10, 10, -5, 5]}

Remember the double-angle formula for cosine:
$\cos \left(2 x\right) = 2 {\cos}^{2} \left(x\right) - 1$

$\cos \left(2 x\right) + 1 = 2 {\cos}^{2} \left(x\right)$
$\frac{1}{2} \cos \left(2 x\right) + \frac{1}{2} = {\cos}^{2} \left(x\right)$
Amplitude = $\frac{1}{2}$
Period = $\pi$
Vertical Shift = up by $\frac{1}{2}$