Question

how many solutions does sin^-1 (0) have on the interval [0,pi)

Answer 1

So.

Inverse sin of zero is asking, at what points on the unit circle is 0 the Y value of a point?

The only place that this would be true is at 0 degrees. 0 degrees has a coordinate of (1, 0), notice how the Y value of 0.

If you're thinking "What about pi??", the equation has a parenthesis on the outside of pi, like this: [0, pi). That means that it can be equal to 0, but must be less than pi. So the only solution is 0 degrees, or 0pi.