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Evaluate the expression  \cos^{-1}(\cos 7)

Option: 1

7


Option: 2

2\pi-7


Option: 3

7-2\pi


Option: 4

None of these


Answers (1)

best_answer

\\\cos^{-1}(\cos 7)\neq 7\because \text{7 is not in the range of } [0,\pi]\\ But\,\,\cos^{-1}(\cos 7)=\cos^{-1}(\cos (2\pi-7))\\ =\cos^{-1}(\cos (7-2\pi))\\ =7-2\pi\\ \because 7-2\pi\text{ lies in the range of } [0,\pi]

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