Question

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

• A. $\frac{7\pi }{6}$
• B. $\frac{5\pi }{6}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{6}$

Answer 1

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

The range of ${\cos }^{-1}x$ is $[0,\pi ]$

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

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

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