Question

Find the principal value of the following:

`sin^-1 (- 1/2)`

Answer 1

`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`