Answer
Exact value of $\sec \frac{7\pi}{6} = -\frac{2\sqrt 3}{3} $
Work Step by Step
To find exact value of $\sec \frac{7\pi}{6}$, let's find its reference angle first.
As $ \frac{7\pi}{6}$ terminates in quadrant III -
The reference angle = $\frac{7\pi}{6} - \pi$ = $\frac{\pi}{6}$
As $ \frac{7\pi}{6}$ terminates in quadrant III, its $\sec$ will be negative. Therefore by reference angle theorem-
$\sec \frac{7\pi}{6}$ = $-\sec\frac{\pi}{6}$
= $-\frac{2}{\sqrt 3}$
= $-\frac{2\sqrt 3}{3}$
