Question

Find the principal value of cos-1$\bigg(\frac {\sqrt3} {2}\bigg)$

Answer 1

Let cos-1$\bigg(\frac {\sqrt3}{2}\bigg)=y$
Then, $cos \,y= \frac {\sqrt3}{2}= cos \bigg(\frac{\pi}{6}\bigg)$
We know that the range of the principal value branch of cos-1 is
[0,π] and cos $\frac{\pi}{6}=\frac{\sqrt3}{2}$

Therefore, the principal value of cos-1 $\bigg(\frac{\sqrt3}{2}\bigg) is \, \frac {\pi}{6}$