Question

What is the domain of `sinx = -1/2`?

Answer 1

Read below.

Explanation:

Let us think...

in terms of all possible values for `x`, there is an infinite number of them.

Specifically, we have:

`sin x=-1/2`

`x=arcsin(-1/2)`

Using our special angles, we see that `arcsin(-1/2)=(11pi)/6`

At the same time, it can equal to `(7pi)/6` because there are two angles that can have the same height. Look below for further understanding.

Now, remember that we could keep adding `2pi` to our answers and still end up with the same sine value.

We have:
`(11pi)/6+2pin`

`(7pi)/6+2pin`

where `n` is an integer.