# How do you find the exact value of cos^-1(-1/2)?

Aug 2, 2016

For 0<= theta<=360°, theta = 120°or 240°

#### Explanation:

cos 60° = 1/2

This is one of the special angles which we should know and recognize.

Hence Cos^-1(1/2) = 60°

However in this case we are working with $\left(- \frac{1}{2}\right)$

From the "CAST" rule, we find that cos is negative in the second and third quadrants.

In the second quadrant, use $180 - \theta$.
In the third use $180 + \theta$.

From 0° to 360° there are two values of theta for
$\theta = C o {s}^{-} 1 \left(- \frac{1}{2}\right)$

theta = 180-60 = 120°

theta = 180+60=240°