Evaluate cos-1(cos 12)

Given cos^-1(cos 12)

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

And here x = 12 which does not lie in the above range.

We know cos (2nπ – x) = cos (x)

Cos (2nπ – 12) = cos (12)

Here n = 2.

Also 4π – 12 belongs in [0, π]

cos^–1(cos 12) = 4π – 12