Answer
$-\frac{1}{2}$
Work Step by Step
RECALL:
In a unit circle,
$\cos{s} = x$
(Refer to Figure 13 on page 111)
The terminal side of the angle $-\frac{5\pi}{6}$ can be located by moving $\frac{5\pi}{6}$ clockwise from the positive x-axis.
This angle has the same terminal side as $\frac{7\pi}{6}$ and intersects intersects the unit circle at the point $(-\frac{\sqrt3}{2}, -\frac{1}{2})$.
This point has $x=-\frac{\sqrt3}{2}$ and $y=-\frac{1}{2}$.
Since $\sin{s}=y$, then
$\sin{(-\frac{5\pi}{6})} =\sin{\frac{7\pi}{6}} = -\frac{1}{2}$
