Question

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

• A. $\frac{\pi }{2}$
• B. $\frac{-\pi }{6}$
• C. $\frac{7\pi }{6}$
• D. $\frac{5\pi }{6}$

Answer 1

The correct option is D

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

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

$={\cos }^{-1}\left(\cos \right(\pi +\frac{\pi }{6}\left)\right)={\cos }^{-1}(-\cos (\frac{\pi }{6}\left)\right)={\cos }^{-1}(-\frac{\sqrt{3}}{2})$
$=\frac{5\pi }{6}$