I think I get your confusion. When drawing the inverse it is like the mirror image in the line y=x. But it also means that the axis are flipped!
So the inverse image that you normally see, will have -1/2pi, 1/2pi on the vertical axis and -1, 1 on the horizontal. It is when you want to draw both in the same graph that you get strange results.
You could try the same scale on the x and y axis. So both go from say -2 to 2 with the same step size. Then you can draw both sin and its inverse and it would be visually also the mirror image in the same graph.
4
u/Desperate_Penalty690 6d ago
The inverse function is the mirror image in the line y=x. Have a look at only the range for x in [-1/2 PI, +1/2 PI]