# How do you evaluate cos(2π/3)?

Nov 5, 2015

$- \frac{1}{2}$

#### Explanation:

This is easy if you know basic angles with radians and the basic values of cosine.

$\pi = 180$ degrees
$2 \pi = 180 \cdot 2$ degrees $= 360$ degrees
$\frac{2 \pi}{3} = \frac{360 \mathrm{de} g r e e s}{3} = 120$ degrees

If you know the unit circle, you know that $\cos \left(120\right)$ is the opposite of $\cos \left(60\right)$ (both in degrees). This is because they are in different quadrants.

Since $\cos \left(60\right) = \frac{1}{2}$
$\cos \left(120\right) = - \frac{1}{2}$

PM me if you don't know how the unit circle works :-).
Hope this helped.