Evaluate each of the following: cos^-1(cos 4π/3)

Question

Evaluate each of the following:

\(cos^{-1}(cos\frac{4\pi}3)\)

Answer 1

The value of cos\((\frac{4\pi}3)\) is \(\frac{-1}2\)

Now,

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

The range of principal value of cos^–1 is [0,π] and cos\((\frac{2\pi}3)=\frac{-1}2\)

Therefore, the value of cos^–1(cos\((\frac{4\pi}3)\)) is \(\frac{2\pi}3\)