Answer
Exact value of $\tan (-\frac{4\pi}{3}) = -\sqrt 3$
Work Step by Step
To find exact value of $\tan (-\frac{4\pi}{3})$, let's find its reference angle first. As $ -\frac{4\pi}{3}$ terminates in quadrant II -
The reference angle = $\frac{4\pi}{3} - \pi$ = $\frac{\pi}{3}$
As $ (-\frac{4\pi}{3})$ terminates in quadrant II, its $\tan$ will be negative. Therefore by reference angle theorem-
$\tan (- \frac{4\pi}{3})$ = - $\tan\frac{\pi}{3}$
= - $\sqrt 3$
