Suppose and . If , then how are related? How are related?
If , then . Therefore, and since .
Is this correct?
Sure, but that's cartesian coordinates. As soon as you start talking about radii and angles (i.e., polar coordinates), the game is different. Example:
In fact, in polar coordinates, the point is the same point as
So from this, you can see that setting
is simply not going to imply that and
Even if you throw in the other equation (the y equation), you're not going to resolve all the ambiguities.