Question

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

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{2\pi }{3}$
• D. $-\frac{\pi }{3}$

Answer 1

Answer: (C)

${\cos }^{-1}\left(\sin \frac{7\pi }{6}\right)={\cos }^{-1}\left[\sin \left(2\pi -\frac{5\pi }{6}\right)\right]$
$={\cos }^{-1}\left[-\sin \frac{5\pi }{6}\right]$
$={\cos }^{-1}\left[-\sin \left(\frac{\pi }{2}+\frac{\pi }{3}\right)\right]$ $={\cos }^{-1}\left[-\cos \frac{\pi }{3}\right]$
$=\pi -\frac{\pi }{3}=\frac{2\pi }{3}$