Question

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

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

Answer 1

The correct option is D $\frac{5\pi }{6}$

For, ${\cos }^{-1}x$,

$x\in [0,\pi ]$

Hence,

${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)={\cos }^{-1}\left(\cos (2\pi -\frac{5\pi }{6})\right)$

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