Answer
$-\frac{1}{2}$
Work Step by Step
$\frac{7\pi}{6}$ radians= $\frac{7\times180}{6}^{\circ}=210^{\circ}$
$210^{\circ}$ is in the third quadrant and sine function is negative in the third quadrant.
As $\theta$ is in quadrant III, the reference angle is
$\theta'=
\theta-180^{\circ}=210^{\circ}-180^{\circ}=30^{\circ}$
$\sin\frac{7\pi}{6}=\sin210^{\circ}=-\sin30^{\circ}=-\frac{1}{2}$
