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Question
The principal value of `cos^-1 (- 1/2)` is ______.
Solution
The principal value of `cos^-1 (- 1/2)` is `(2pi)/3`.
Explanation:
Let `cos^1 (- 1/2)` = x
⇒ cos x = `-1/2`
⇒ cos x = `cos(- pi/3)`
⇒ cos x = `cos(pi - pi/3)`
= `cos (2pi)/3`
∴ x = `(2pi)/3 ∈ [0, pi]`
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