# Cosine of 120 Degrees

## Theorem

$\cos 120^\circ = \cos \dfrac {2 \pi} 3 = - \dfrac 1 2$

where $\cos$ denotes cosine.

## Proof

 $$\displaystyle \cos 120^\circ$$ $$=$$ $$\displaystyle \cos \left({90^\circ + 30^\circ}\right)$$ $$\displaystyle$$ $$=$$ $$\displaystyle - \sin 30^\circ$$ Cosine of Angle plus Right Angle $$\displaystyle$$ $$=$$ $$\displaystyle - \frac 1 2$$ Sine of 30 Degrees

$\blacksquare$