Question

How do you evaluate `arcsin^-1(-1/2)` without a calculator?

Answer 1

`theta = 11/6 pi = 330^@`

Explanation:

Given: `arcsin^-1 (-1/2)`

I believe what you want is `arcsin (-1/2) = sin^-1(-1/2)`

`arcsin (-1/2)` says, find me the angle that has a sine `= -1/2`,

or what is the angle `theta` that yields `sin theta = -1/2`?

Since the `arcsin` function has a limited domain: `-pi/2 <= theta <= pi/2`, we will only need to look at the 4th quadrant due to the negative sign.

`theta = 11/6 pi = 330^@`