# How do you evaluate arc cos(-1/2)?

Nov 26, 2016

$\arccos \left(- \frac{1}{2}\right) = \frac{2 \pi}{3}$

#### Explanation:

$\arccos x$ is an angle whose cosine ratio is $- \frac{1}{2}$.

Now as $\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$ and $\cos \left(\pi - A\right) = - \cos A$

$\cos \left(\pi - \frac{\pi}{3}\right)$ i.e. $\cos \left(\frac{2 \pi}{3}\right) = - c o e \left(\frac{\pi}{3}\right) = - \frac{1}{2}$

As $\cos \left(\frac{2 \pi}{3}\right) = - \frac{1}{2}$, we have

$\arccos \left(- \frac{1}{2}\right) = \frac{2 \pi}{3}$