Question

when solving question cos(cos inverse minus root 3 divided by 2) we get the answer = minus root 3 divided by 2 which is equal to minus pie divided by 3 .And minus pie divided by 3 does not belong to (0,pie) which is the principal branch of cos inverse.

How to change minus pie divided by 3 so that the answer can belong to (0,pie)

Answer 1

$$\begin{gathered} \cos \left(\frac{5\mathrm{\pi }}{6}\right)=-\frac{\sqrt{3}}{2} \\ And,\frac{5\mathrm{\pi }}{6}\in \left(0,\mathrm{\pi }\right) \\ Therefore, \\ {\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)={\cos }^{-1}\left(\cos \frac{5\mathrm{\pi }}{6}\right)=\frac{5\mathrm{\pi }}{6} \end{gathered}$$