if x/2=sin(theta), then does theta=arcsin(x/2)? If not, what does theta equal?

Answer 1

sin θ = (x/2)
θ = sin^(-1) (x/2)
or
θ = arc sin (x/2)
In words, θ is the angle whose sine is x/2

Answer 2

It will if -pi/2<=theta<=pi/2. Otherwise it won't (remember that sin(x) is periodic and you have to make sure you are in the right period).

Answer 3

Absolutely yes.