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Question
The value of `cos^-1 (cos (14pi)/3)` is ______.
Solution
The value of `cos^-1 (cos (14pi)/3)` is `(2pi)/3`.
Explanation:
`cos^-1 (cos (14pi)/3) ≠ (14pi)/3` as `(14pi)/3 ∉ [0, pi]`
∴ `cos^-1 (cos (14pi)/3) = cos^-1 cos(4pi + (2pi)/3)`
= `cos^-1 cos (2pi)/3` .....`(because cos(2"n"pi + theta) = cos theta)`
= `(2pi)/3` ......`(because cos^-1 (cos x) = x, x ∈ [0, pi])`
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