Question

Evaluate ${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)$

Answer 1

We have,

${\cos }^{-1}\left(\cos \left(\frac{7\pi }{6}\right)\right)$

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

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

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

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

$=\pi -\frac{\pi }{6}$

$=\frac{5\pi }{6}$

Hence, the value is $\frac{5\pi }{6}$.