Question

Find the value of ${\cos }^{-1}\left(\cos \frac{13\mathrm{\pi }}{6}\right)$

Answer 1

$$\begin{gathered} {\cos }^{-1}\left(\cos \frac{13\mathrm{\pi }}{6}\right)={\cos }^{-1}\left[\cos \left(2\mathrm{\pi }+\frac{\mathrm{\pi }}{6}\right)\right] \\ ={\cos }^{-1}\left[\cos \left(\frac{\mathrm{\pi }}{6}\right)\right] \\ =\frac{\mathrm{\pi }}{6} \end{gathered}$$