Question

What is sin^−1(-√3 / 2)?

Answer 1

`sin^-1(sqrt3/2) = 240° or 300°`

Explanation:

A right-angled triangle with angles of `60°and 30°` has sides in the ratio `1 : sqrt3 : 2`

The core angle of `sqrt3/2` is `60°`

However, the negative sign indicates that we are working with an angle in the `3rd or 4 th` quadrants.

In the `3rd` quadrant: `theta = 180° + 60° = 240°`

In the `4 th` quadrant: `theta = 360°-60° =300°`

`sin^-1(sqrt3/2) = 240° or 300°`

Check using a calculator.

`sin 240° = -0.866`
`sin 300° = -0.866`

`-sqrt3/2 = -0.866`