Evaluate each of the following:

cos^{–1}(cos 5)

cos^{–1}(cos x) = x

Provided x ϵ [0,π] ≈ [0,3.14]

And in our equation x is 5 which does not lie in the above range.

We know cos[2π – x] = cos[x]

∴ cos(2π – 5) = cos(5)

Also 2π–5 belongs in [0,π]

∴ cos^{–1}(cos 5) = 2π–5

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