Answer
$\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4}, \frac{7\pi}{4}$
Work Step by Step
1. Given $cos^2(s)=\frac{1}{2}$, we have $cos(s)=\pm\frac{\sqrt 2}{2}$.
2. For $cos(s)=\frac{\sqrt 2}{2}$, we can find a reference angle as $s_0=cos^{-1}(\frac{\sqrt 2}{2})=\frac{\pi}{4}$. In $[0,2\pi)$, there are two solution angles $s=\frac{\pi}{4}, 2\pi-\frac{\pi}{4}$ or $s=\frac{\pi}{4}, \frac{7\pi}{4}$
3. For $cos(s)=-\frac{\sqrt 2}{2}$, we can find a reference angle as $s_0=cos^{-1}(\frac{\sqrt 2}{2})=\frac{\pi}{4}$. In $[0,2\pi)$, there are two solution angles $s=\pi-\frac{\pi}{4}, \pi+\frac{\pi}{4}$ or $s=\frac{3\pi}{4}, \frac{5\pi}{4}$
4. The solutions are $\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4}, \frac{7\pi}{4}$
