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Question
Find the principal value of the following: sin-1 `(1/sqrt(2))`
Solution
The principal value branch of sin-1x is `[- pi/2, pi/2]`.
Let sin-1`(1/sqrt(2)) = α, "where" (-pi)/(2) ≤ α ≤ pi/(2)`
∴ sin α = `(1)/(sqrt2) = sin pi/(4)`
∴ α = `pi/(4) ...[∵ - pi/2 ≤ pi/4 ≤ pi/2 ]`
∴ the principal value of sin-1`(1/sqrt(2)) "is" pi/(4)`.
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