Drag the point, "A" along the sine function. Notice that A's reflection about the line y = x (point "A'") traces out the inverse, which is not a function, since it clearly violates the vertical line test (as you'd expect, given the periodic nature of the sine function -- "It's NOT one-to-one!")
However, if you limit the domain of the sine function has been done with point "B" and its image "B'". Drag the "Inverse" slider to see one possible inverse solution.

This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.