# How do you find the exact value for cos 240?

May 24, 2015

it equals $\left(- \frac{1}{2}\right)$ because $\cos \left({60}^{\circ}\right) = \frac{1}{2}$

#### Explanation:

The reference angle for ${240}^{\circ}$ is ${60}^{\circ}$ (since ${240}^{\circ} = {180}^{\circ} + {60}^{\circ}$)

${60}^{\circ}$ is an angle of one of the standard triangles with
$\cos \left({60}^{\circ}\right) = \frac{1}{2}$

${240}^{\circ}$ is in the 3rd quadrant so (either by CAST or noting that the "x-side" of the associate triangle is negative)
$\cos \left({240}^{\circ}\right) = - \cos \left({60}^{\circ}\right)$

$\cos \left({240}^{\circ}\right) = - \frac{1}{2}$