Answer
Exact value of $\csc (-\frac{5\pi}{6})= -2$
Work Step by Step
To find exact value of $\csc (-\frac{5\pi}{6})$, let's find its reference angle first.
As $ -\frac{5\pi}{6}$ terminates in quadrant III -
The reference angle = $(-\frac{5\pi}{6}) + \pi$ = $\frac{\pi}{6}$
As $ (-\frac{5\pi}{6})$ terminates in quadrant III, its $\csc$ will be negative. Therefore by reference angle theorem-
$\csc (- \frac{5\pi}{6})$ = $-\csc\frac{\pi}{6}$
= $-2$
