Answer
$-\frac{\sqrt 2}{2}$
Work Step by Step
Since sine is an odd function, $\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})$
Using the unit circle, $\frac{3\pi}{4}$ falls in the second quadrant, where sine is positive.
By using the identity $\sin(\pi-\theta)=\sin(\theta)$,
$-\sin(\frac{3\pi}{4})=-\sin(\pi-\frac{\pi}{4})=-\sin(\frac{\pi}{4})$
$\frac{\pi}{4}$ is a special angle,
$-\sin(\frac{\pi}{4})=-\frac{\sqrt 2}{2}$
Therefore,
$\sin(-\frac{3\pi}{4})=-\frac{\sqrt 2}{2}$