# How do you find the exact value of sin^-1(cos(pi/6))?

$\frac{\pi}{3}$
${\sin}^{- 1} \cos \left(\frac{\pi}{6}\right) = {\sin}^{- 1} \sin \left(\frac{\pi}{2} - \frac{\pi}{6}\right) = \frac{\pi}{2} - \frac{\pi}{6} = \frac{\pi}{3}$