Operating system: Windows 10 Home
Graphics card: Intel Iris XE

Broken: 3.0 b
Worked: N/A

So I am trying to calculate texture coordinates that go around a sphere on the X axis and up the sphere on the Y. Don't get me wrong, I know that you can already set Image Texture nodes to sphere coords. But what I am trying to do is to use a spherical cage to catch caustics from an object, bake to a texture, and project them back from that object, so to do that I would need to calculate those sphere coordinates from the offset between where the incoming ray was from and the position of the object. But you can't just put that into an image texture node and have textures bake from those coordinates, and you have to use Generated output of a tex coord node for the sphere setting to work.

The problem is that I'm trying to use a Vector Math node set to dot product, and I'm getting this stretching on part of the textures. It's almost like it's not linear angle. And I don't know what goofy math I would need to bring these values back to what they should be. I've tried Power, Square Root, Inverse Square, Sine of the value * (pi / 4), everything under the sun. Is this just how dot product is supposed to function?

Exact steps for others to reproduce the error
Based on the default startup or an attached .blend file (as simple as possible).