How do you evaluate cos^-1(1/2) without a calculator?

Jan 2, 2017

${\cos}^{- 1} \left(- \frac{1}{2}\right) = {120}^{\circ}$

Explanation:

See from tables relating to trigonometric ratios of special angles ass shown in figure below

we have $\cos {120}^{\circ} = - \frac{1}{2}$ and $\cos {240}^{\circ} = - \frac{1}{2}$

However range for $\theta = {\cos}^{- 1} x$ is $0 < \theta < \pi$

Hence, ${\cos}^{- 1} \left(- \frac{1}{2}\right) = {120}^{\circ}$.