Evaluate each of the following:

cos^{–1}(cos 4)

cos^{–1}(cos x) = x

Provided x ϵ [0,π] ≈ [0,3.14]

And in our equation x is 4 which does not lie in the above range.

We know cos[2π – x] = cos[x]

∴ cos(2π – 4) = cos(4)

Also 2π–4 belongs in [0,π]

∴ cos^{–1}(cos 4) = 2π–4

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