Why did you invert the axis?
Okay, so I have a rectangular coordinate system where the y axis is inverted... So in this right is positive x and down is positive y.
I need to be able convert from this system to polar coordinates and back again, but in smaller steps, not in some big formula, because this is for programming.
How would I do this?
Because in computers, everything is done from the top left to the bottom right. I could have made my program use Cartesian coordinates and then translate them to the inverted y axis system every time I want to render it on the screen, but I chose not to.
I think wikipedia does a better job than anyone at explaining the conversion: Polar coordinate system - Wikipedia, the free encyclopedia
Now, about the inverting. My suggestion is invert the polar angle as well. Instead of counterclockwise being positive, make clockwise positive.
This way the conversion formula is exactly the same as the normal polar to rectangular.