Evaluate the following: ^ -1 ( 5) - Vidyadip

Question

Evaluate the following:
$\cos^{-1}(\cos5)$

✓

Answer

$\cos^{-1}(\cos\text{x})=\text{x}$
provided $\text{x}\in [0,\pi]\approx[0,3.14]$
And in our equation X is 5 which does not lie in the above range.
We know $\cos [2\pi -\text{x}]=\cos[\text{x}]$
$\therefore \cos (2\pi -5)=\cos (5)$
Also $2\pi -5$ belongs in $[0,\pi]$
$\therefore \cos^{-1}(\cos 5)=2\pi -5$

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