# How do you evaluate cos^-1(cos((7pi)/6))?

$= 5 \frac{\pi}{6}$ least value
${\cos}^{-} 1 \left(\cos \left(7 \frac{\pi}{6}\right)\right) = {\cos}^{-} 1 \left(\cos \left(\pi + \frac{\pi}{6}\right)\right) = {\cos}^{-} 1 \left(- \cos \left(\frac{\pi}{6}\right)\right) = {\cos}^{-} 1 \left(\cos \left(\pi - \frac{\pi}{6}\right)\right) = {\cos}^{-} 1 \left(\cos \left(5 \frac{\pi}{6}\right)\right) = 5 \frac{\pi}{6}$