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The value of \cos^{-1}(\cos 4)\\ is

Option: 1

2\pi - 4


Option: 2

4-2\pi


Option: 3

\frac{7\pi}{2}- 4


Option: 4

4-\frac{7\pi}{2}


Answers (1)

best_answer

Graph of Principal Value of function f-1 (f (x))

The graph of y = cos-1(cos (x))

 

\text{We know that 4 radian is not in range of } [0, \pi]

4 lies in (\pi, 2\pi)

So using graph, the value of \cos^{-1}(\cos x) \,\,equals\,\,2\pi-x for this branch

So, \cos^{-1}(\cos 4) will be 2\pi-x = 2\pi-4

Posted by

Devendra Khairwa

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