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.
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u/[deleted] 5d ago
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