Answer
$-\frac{\sqrt 2}{2}$
Work Step by Step
As $-\frac{3\pi}{4}$ is coterminal with $-\frac{3\pi}{4}+2\pi$, we can write
$\cos (-\frac{3\pi}{4})=\cos(-\frac{3\pi}{4}+2\pi)=\cos \frac{5\pi}{4}$
$=\cos (\pi+\frac{\pi}{4})=-\cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$
(We used the relation $\cos (\pi+x)=-\cos x$ here.)
