Question

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

• A. $\frac{5\pi }{3}$
• B. $\frac{7\pi }{6}$
• C. $\frac{\pi }{3}$
• D. None of these

Answer 1

Answer: (C)

We have.
${\cos }^{-1}\left(-\sin \frac{7\pi }{6}\right)={\cos }^{-1}\left(-\sin \left(\pi +\frac{\pi }{6}\right)\right)$
$={\cos }^{-1}\left(\sin \frac{\pi }{6}\right)$
$=\frac{\pi }{2}-{\sin }^{-1}\left(\sin \frac{\pi }{6}\right)=\frac{\pi }{2}-\frac{\pi }{6}=\frac{\pi }{3}$