Evaluate cos-1(cos 4)

Given cos^-1(cos 4)

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

And here x = 4 which does not lie in the above range.

We know that cos (2π – x) = cos(x)

Thus, cos (2π – 4) = cos (4) so 2π–4 belongs in [0, π]

Hence cos^–1(cos 4) = 2π – 4