Question

Find the principle value of ${\cos }^{-1}\left[\cos \left(\frac{7\pi }{3}\right)\right]$.

Answer 1

$\cos \frac{7\pi }{3}=\cos (2\pi +\frac{\pi }{3})=\cos \frac{\pi }{3}$

As $-\frac{\pi }{2}\le \frac{\pi }{3}\le \frac{\pi }{2}$

$\Rightarrow {\cos }^{-1}\left(\cos \frac{\pi }{3}\right)=\frac{\pi }{3}$.