#### Answer

Please see below.

#### Work Step by Step

Please note that according to the identity $\cos^2x=\frac{1}{2}+ \frac{1}{2}\cos 2x$, the graph of $y= \cos^2x$ (the red graph) is the graph of $y=\cos 2x$ (the blue graph) vertically shrunk by a factor of $\frac{1}{2}$ and then shifted up $\frac{1}{2}$ unit.
The period of $y=\cos^2x$ equals the period of $\cos 2x$, that is $\frac{2 \pi }{2}=\pi$.