Evaluate each of the following: cos^-1(cos 5π/4)

Question

Evaluate each of the following: 

\(cos^{-1}(cos\frac{5\pi}4)\)

Answer 1

The value of \(cos(\frac{5\pi}4)\) is \(\frac{-1}{\sqrt2}\)

Now, 

∴ The question becomes \(cos^{-1}(\frac{-1}{\sqrt2})\)

Let \(cos^{-1}(\frac{-1}{\sqrt2})\) = y

The range of principal value of cos^–1 is [0,π] and cos\((\frac{3\pi}4)=\frac{-1}{\sqrt2}\)

Therefore, the value of cos^–1(cos\((\frac{5\pi}4)\)) is \(\frac{3\pi}4.\)