Question

How do you find the exact value of `arcsin (-1/2)`?

Answer 1

`-pi/6`

Explanation:

Arcsin can be thought of as the ANGLE with the specified value of sin.

The range of `arcsin` or `sin^-1` is `pi/2` to `-pi/2`.

Arcsin of a positive value is found in QI or zero to `pi/2`.
Arcsin of a negative value is found in QIV or zero to `-pi/2`

In this case, `arcsin(-1/2)` is found in QIV. The angle with a sin of `-1/2` in QIV is `-pi/6`.