Answer
Exact value of $\csc \frac{5\pi}{4} = -\sqrt 2$
Work Step by Step
To find exact value of $\csc \frac{5\pi}{4}$, let's find its reference angle first.
As $ \frac{5\pi}{4}$ terminates in quadrant III -
The reference angle = $\frac{5\pi}{4} - \pi$ = $\frac{\pi}{4}$
As $ \frac{5\pi}{4}$ terminates in quadrant III, its $\csc$ will be negative. Therefore by reference angle theorem-
$\csc \frac{5\pi}{4}$ = $-\csc\frac{\pi}{4}$
= $-\sqrt 2$
