Fantastic,it works. I knew it was a small mistake. I spend so many times on it. FYI, the function Psi is quite long and complicated to write as it is a Thebychev-Fourier serie. Many thanks.
Difficult to say much without complete code e.g. a definition of the actual function psi[t,theta]. My guess is you want to define
psi[t,theta]
r[x_,y_]: Sqrt[x^2 + y^2] theta[x_,y_]:= ArcTan[x, y]
and then plot ContourPlot[\[Psi][r[x,y],theta[x,y]],....
ContourPlot[\[Psi][r[x,y],theta[x,y]],...
Need to argument form of ArcTan returns angle values between minus pi and pi. Try
ArcTan[-1,1]
The statement that you are quoting from the documentation is referring to the single argument form.
