Thanks so mush for your help.
plots:-densityplot(f, theta=0..2*Pi, r=r1 .. r2, coords=polar, colorstyle = HUE, style = patchnogrid);
By above program, first, initialize theta, the coordinate system seems to be in cartesian because the horizontal axis becomes the value for theta and vertical axis becomes the values for r.
when r is a constant we have figure below for my function f(r, theta), r=0.3..0.5 and theta=0..2*pi
In this figure, f(r, theta) is shown by color in circle (symmetric) in polar coordinate
when r is a function of theta, we expect f(r, theta) is shown by color in circle (nonsymmetric) r=0.3+0.1*cos(theta)..0.5*0.1*cos(theta) and theta=0..2*pi like this
How can I plot it?