Evaluate each of the following: cos^-1(cos 13π/6)

Question

Evaluate each of the following:

\(cos^{-1}(cos \frac{13π}6)\)

Answer 1

The value of cos\((\frac{13\pi}6)\) is \(\frac{\sqrt3}2\)

Now,

∴ The question becomes cos^–1\((\frac{\sqrt 3}2)\)

The range of principal value of cos^–1 is [0,π] and cos\((\frac{\pi}6)=\frac{\sqrt3}2\)

Therefore, the value of cos^–1(cos\((\frac{13\pi}6)\)) is \(\frac{\pi}6.\)