Answer
$$ - \frac{1}{2}$$
Work Step by Step
$$\eqalign{
& \cos \frac{{2\pi }}{3} \cr
& {\text{Write }}\frac{{2\pi }}{3}{\text{ as }}\pi - \frac{\pi }{3} \cr
& \cos \frac{{2\pi }}{3} = \cos \left( {\pi - \frac{\pi }{3}} \right) \cr
& {\text{Use the identity cos}}\left( {\pi - \theta } \right) = - \cos \theta \cr
& \cos \frac{{2\pi }}{3} = - \cos \left( {\frac{\pi }{3}} \right) \cr
& {\text{From the unit circle we known that cos}}\frac{\pi }{3} = \frac{1}{2},{\text{ then}} \cr
& \cos \frac{{2\pi }}{3} = - \frac{1}{2} \cr} $$
