### Instruction: Find $\cos \frac{5 \pi}{4}.$.### Response: So we need to find $\cos \frac{5 \pi}{4}$.
$\cos \frac{5 \pi}{4}$ is the same as $\cos \left(\pi + \frac{\pi}{4}\right)$.
Right. So that means that $\cos \frac{5 \pi}{4} = -\cos \frac{\pi}{4}$.
$\cos \frac{\pi}{4}$ is equal to $\frac{\sqrt{2}}{2}$, so $-\cos \frac{\pi}{4} = -\frac{\sqrt{2}}{2}$.