Answer
$\frac{\sqrt 2}{2}$
Work Step by Step
Since sine is an odd function, $\sin(-\frac{7\pi}{4})=-\sin(\frac{7\pi}{4})$
Using the unit circle, $\frac{7\pi}{4}$ is in the fourth quadrant, where sine is negative.
Using the identity $\sin(2\pi-\theta)=-\sin(\theta)$,
$-\sin(\frac{7\pi}{4})=-\sin(2\pi-\frac{\pi}{4})=\sin(\frac{\pi}{4})$
$\frac{\pi}{4}$ is a special angle,
$\sin(\frac{\pi}{4})=\frac{\sqrt 2}{2}$
Therefore,
$\sin(-\frac{7\pi}{4})=\frac{\sqrt 2}{2}$
