Question

What will be the principal value of `sin^-1(-1/2)`?

Options

• `(- pi)/2`

• `pi/3`

• `(- pi)/4`

• `(- pi)/6`

Answer 1

`(- pi)/6`

Explanation:

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

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

= `- sin(pi/6) = sin(- pi/6)`

Range of the principal of `sin^-1x` is

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

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