Answer
Exact value of $\cos \frac{4\pi}{3} = -\frac{1}{2}$
Work Step by Step
To find exact value of $\cos \frac{4\pi}{3}$, let's find its reference angle first. As $ \frac{4\pi}{3}$ terminates in quadrant III,
The reference angle = $\frac{4\pi}{3} - \pi$ = $\frac{\pi}{3}$
As $ \frac{4\pi}{3}$ terminates in quadrant III, its $\cos$ will be negative. Therefore by reference angle theorem-
$\cos \frac{4\pi}{3}$ = - $\cos\frac{\pi}{3}$
= - $\frac{1}{2}$
