Using polar coordinate to sketch the graph of a function

Question

I want to sketch the following function, $f(x,y)=\frac{x^2-y^2}{x^2+y^2}$, that is , $z=\frac{x^2-y^2}{x^2+y^2}$. By using polar coordinate, $ z=f(\theta)=\cos(2\theta)$. I think the next step I should rotate it around z-axis. Is that correct? If so, how I can do that? Is there another way to do the sketch without the polar coordinate?

Answer 1

@00GB please get familiar with a tool that plots anything you want in 3d. The following is done with python: