Answer
$\sin \frac{-7\pi}{6}=\frac{-1}{2}$
Work Step by Step
We are given $\sin \frac{-7\pi}{6}$
$\sin(\frac{-7\pi}{6}+\pi)=\sin(\frac{-\pi}{6})$
convert $\frac{\pi}{6}$ radians to degrees
$\frac{\pi}{6}=\frac{\pi}{6}(\frac{180^\circ}{\pi})$
$\frac{\pi}{6}=30^\circ$
$\sin \frac{-7\pi}{6}=-(\sin 30^\circ)$
$\sin30^\circ=\frac{1}{2}$
so $\sin \frac{-7\pi}{6}=\frac{-1}{2}$