Question

Find the principal value of ${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Answer 1

Let ${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)=y$.

Then, $\cos y=\frac{\sqrt{3}}{2}=\cos \left(\frac{\pi }{6}\right)$.
We know that the range of the principal value of ${\cos }^{-1}$ is $[0,\pi ]$ and $\cos \left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}$.
Therefore, the principal value of ${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is $\frac{\pi }{6}.$