Answer
$\frac{\pi}{4}$
Work Step by Step
$\frac{7\pi}{4}$ is coterminal with $(\frac{7\pi}{4}-2\pi)=-\frac{\pi}{4}$:
$\cos\frac{7\pi}{4}=\cos(-\frac{\pi}{4})=\cos\frac{\pi}{4}$
Then, $\cos^{-1}(\cos \frac{7\pi}{4})=\cos^{-1}(\cos\frac{\pi}{4})$
Within the restricted interval ($0\leq\theta\leq\pi$),
$\cos^{-1}(\cos\theta)=\theta$
Therefore, $\cos^{-1}(\cos \frac{\pi}{4})=\frac{\pi}{4}$
