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Question
Find the principal value of the following:
`sin^-1 (- 1/2)`
Solution
`sin^-1 (- 1/2)`
Let `sin^-1 (- 1/2)` = y
`["where" (-pi)/2 <= y <= pi/2]`
`- 1/2` = sin y
sin y = `- 1/2` ...`(∵ sin pi/6 = 1/2)`
`sin y = sin(- pi/6) ...[∵ sin (- pi/6) = - sin (pi/6)]`
∴ y = `- pi/6`
∴ The principal value of sin-1 `(- 1/2) "is" - pi/6`
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