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

$\frac{\pi}{3}$
 color(red)(cos^(-1)(costheta)=theta,..thetain[0,pi]
We know that, $\frac{1}{2} = \cos \left(\frac{\pi}{3}\right) \mathmr{and} \frac{\pi}{3} \in \left[0 , \pi\right]$
$\implies {\cos}^{- 1} \left(\frac{1}{2}\right) = {\cos}^{- 1} \left(\cos \left(\frac{\pi}{3}\right)\right) = \frac{\pi}{3}$