Evaluate the following: ^ -1 ( 4) - Vidyadip

Question

Evaluate the following:
$\cos^{-1}(\cos4)$

✓

Answer

We know that,
$\cos^{-1}\big(\cos\theta\big)=\begin{cases}-\theta,&\text{if }\theta\in[-\pi,0]\\\theta,&\text{if }\theta\in[0,\pi]\\2\pi-\theta,&\text{if }\theta\in[\pi,2\pi]\\-2\pi+\theta,&\text{if }\theta\in[2\pi,3\pi]\end{cases}$
We have
$\cos^{-1}(\cos4)=\cos^{-1}\{\cos(2\pi-4)\}=2\pi-4$

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