#### Answer

$\color{blue}{\sin{(\frac{7\pi}{6})}=-\frac{1}{2}}$

#### Work Step by Step

Figure 13 on page 579 of this book shows that the unit circle point $(-\frac{\sqrt3}{2}, -\frac{1}{2})$ corresponds to the real number $\dfrac{7\pi}{6}$.
RECALL:
(i) $\cos{s} = x$
(ii) $\sin{s} = y$
(iii) $\tan{s}=\dfrac{y}{x}$
Use the coordinates of the unit circle point above and the formula in (ii) above to obtain:
$\color{blue}{\sin{(\frac{7\pi}{6})}=-\frac{1}{2}}$