Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 521: 108

See graph.

To obtain the graph of $g(x)=cos^2(x)=\frac{1+cos(2x)}{2}$ from one period of $y=cos(x)$, compress the curve horizontally by a factor of $1/2$, compress vertically by a factor of $1/2$, then shift up $1/2$ unit. Repeat the resulting curve horizontally to cover the window of $[0,2\pi]$. See graph.