Plot a function in polar coordinates, not PolarPlot

Questions
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1

Hello,
How to plot a function [contours, or density] say in 2D, but that is expressed in polar coordinates (r and phi) and not cartesian coordinates which are taken automatically by the notebook?
Example

f = r^2 Cos [phi], {r,-5,5}, {phi,0, 2 Pi}

When I do that, the notebook automatically assumes r and phi to be the cartesian coordinates x and y!

2

Hello Rabih Sultan,

one obvious way would be expressing r and phi in cartesian coordinates:

f[r_, phi_] := r^2 Cos[phi]
ContourPlot[f[Norm[{x, y}], ArcTan[x, y]], {x, -5, 5}, {y, -5, 5}, RegionFunction -> (Norm[{#1, #2}] < 5 &)]

1.png
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3

Thank you very much. That was quite helpful.
Rabih