Question

Find the principal value of the following:

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

Answer 1

Let `sin^(-1) (-1/2)` = y

Then sin y = `-1/2 = -sin(pi/6) = sin(-pi/6)`

We know that the range of the principal value branch of sin⁻¹ is

`[-pi/2, pi/2]` and `sin (-pi/6) = - 1/2,`

Where `-pi/6 ∈ [-pi/2,pi/2]`

Therefore, the principal value of `sin^(-1) (-1/2)` is `-pi/6`.