Question

Find principle value of ${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}\left(0\right)$

Answer 1

Value of the function ${\sin }^{-1}x$ , lies in the interval $[-\frac{\pi }{2},\frac{\pi }{2}]$

So, ${\sin }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{6}$

Value of the function${\cos }^{-1}x$ lies in the interval $[0,\pi ]$

So, ${\cos }^{-1}\left(0\right)=\frac{\pi }{2}$

Now,

${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}\left(0\right)=\frac{\pi }{6}+\frac{\pi }{2}=\frac{2\pi }{3}$