Answer
$\sin \frac{7\pi}{4}=\frac{-\sqrt 2}{2}$
Work Step by Step
We are given $\sin \frac{7\pi}{4}$
convert $\frac{7\pi}{4}$ to degrees
$\frac{7\pi}{4}$ radians=$\frac{7\pi}{4}(\frac{180^\circ}{\pi})$
$\frac{7\pi}{4}$ radians= $315^\circ$
$\sin 315^\circ=\frac{-\sqrt 2}{2}$
so $\sin \frac{7\pi}{4}=\sin315^\circ=\frac{-\sqrt 2}{2}$