Evaluate cos-1(cos 5)

Given cos^-1(cos 5)

We have cos^–1(cos x) = x if x ϵ [0, π] ≈ [0, 3.14]

And here x = 5 which does not lie in the above range.

We know that cos (2π – x) = cos(x)

Thus, cos (2π – 5) = cos (5) so 2π–5 belongs in [0, π]

Hence cos^–1(cos 5) = 2π – 5