# How do you evaluate cos^-1(sin(pi/6))?

$\frac{\pi}{3.}$
$\sin \left(\frac{\pi}{6}\right) = \cos \left(\frac{\pi}{2} - \frac{\pi}{6}\right) = \cos \left(\frac{\pi}{3}\right)$
$\therefore {\cos}^{-} 1 \left(\sin \left(\frac{\pi}{6}\right)\right) = {\cos}^{-} 1 \left(\cos \left(\frac{\pi}{3}\right)\right) = \frac{\pi}{3.}$
as ${\cos}^{-} 1$ and $\cos$ are inverses of each other, their composition is the Identity Fun, i.e., cos^-1(costheta))=theta, if $\theta \in \left[o , \pi\right] ,$ and, $\cos \left({\cos}^{-} 1 x\right) = x . \mathmr{if} | x | \le 1.$