Answer
-0.5
Work Step by Step
Since cosine is an even function, $\cos(-\frac{4\pi}{3})=\cos(\frac{4\pi}{3})$
$\frac{4\pi}{3}$ is an angle found in the third quadrant of the unit circle, where cosine is negative.
By using the identity $\cos(\pi+\theta)=-\cos(\theta)$,
$\cos(\frac{4\pi}{3})=\cos(\pi+\frac{\pi}{3})=-\cos(\frac{\pi}{3})$
As $\frac{\pi}{3}$ is a special angle,
$-\cos(\frac{\pi}{3})=-0.5$
Therefore,
$\cos(-\frac{4\pi}{3})=-0.5$
