I wondered if anyone could explain why arcsinx (sin^-1 x) has a limit on y of -pi/2≤ y ≤ pi/2?
Look at the graph of the sine function, and keep in mind the Horizontal Line Test for determining if a function is invertible.
If you take the whole sine wave, can you get an invertible function? No; clearly not.
If you take one small part of the wave, from a "trough" point to a "peak" point, can you get an invertible function?