\documentclass{article}
\usepackage{pst-plot}
\makeatletter
% D.G. addition - Jun.  9, 1998 - Polar plots using the \psplot macro
% Code added according the way suggested by Ulrich Dirr <udirr@das-team.com>
% USW 03/09/03: the valid email address is of course now <ud@art-satz.de>

% For polar plots
\newif\ifpolarplot
\def\psset@polarplot#1{\@nameuse{polarplot#1}}
\psset@polarplot{false}

\def\psplot@i#1#2#3{%
  \pst@killglue
  \begingroup
    \use@par
    \@nameuse{beginplot@\psplotstyle}%
% D.G. modification begin - Jun.  9, 1998
    \ifpolarplot
      \addto@pscode{%
        \psplot@init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk@plotpoints div def
        /xy {% Adapted from \parametricplot@i
          #3 dup x cos mul exch x sin mul
          \pst@number\psxunit mul exch
          \pst@number\psyunit mul exch
        } def}%
    \else
% D.G. modification end
      \addto@pscode{%
        \psplot@init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk@plotpoints div def
        /xy {
          x \pst@number\psxunit mul
          #3 \pst@number\psyunit mul
        } def}%
% D.G. modification begin - Jun.  9, 1998
    \fi
% D.G. modification end
    \gdef\psplot@init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \psplot@ii
    \else
      \psplot@iii
    \fi
  \endgroup
  \ignorespaces}

\makeatother

\pagestyle{empty}

\begin{document}

% Examples from Ulrich Dirr <udirr@das-team.com>
% USW 03/09/03: the valid email address is of course now <ud@art-satz.de>

\footnotesize

\psset{plotpoints=200}

\begin{pspicture}*(-5,-5)(3,3)
  \psaxes[labelsep=.75mm,arrowlength=1.75,ticksize=2pt,linewidth=0.17mm]%
         {->}(0,0)(-4.99,-4.99)(3,3)
  \rput[Br](3,-.35){$x$}
  \rput[tr](-.15,3){$y$}
  \rput[Br](-.15,-.35){$0$}
  %
  \psset{linewidth=.35mm,polarplot=true}
  \psplot{140}{310}{3 neg x sin mul x cos mul x sin 3 exp x cos 3 exp add div}
  \psplot{140}{310}{6 neg x sin mul x cos mul x sin 3 exp x cos 3 exp add div}
  \psplot{140}{310}{9 neg x sin mul x cos mul x sin 3 exp x cos 3 exp add div}
\end{pspicture}
\hfill
\begin{pspicture}(-2.5,-2.5)(2.5,2.5)
  \psaxes[labelsep=.75mm,arrowlength=1.75,ticksize=2pt,linewidth=0.17mm]%
         {->}(0,0)(-2.5,-2.5)(2.5,2.5)
  \rput[Br](2.5,-.35){$x$}
  \rput[tr](-.15,2.5){$y$}
  \rput[Br](-.15,-.35){$0$}
  %
  \psset{linewidth=.35mm,plotstyle=curve,polarplot=true}
  \psplot{0}{360}{x cos 2 mul x sin mul}
  \psplot{0}{360}{x cos 3 mul x sin mul}
  \psplot{0}{360}{x cos 4 mul x sin mul}
\end{pspicture}

\vspace{1cm} \psset{unit=0.5}
\begin{pspicture}(-8.5,-8.5)(9,9)
  \psaxes[Dx=2,dx=2,Dy=2,dy=2,labelsep=.75mm,arrowlength=1.75,ticksize=2pt,
          linewidth=0.17mm]{->}(0,0)(-8.5,-8.5)(9,9)
  \rput[Br](9,-.7){$x$}
  \rput[tr](-.3,9){$y$}
  \rput[Br](-.3,-.7){$0$}
  %
  \psset{linewidth=.35mm,plotstyle=curve,polarplot=true}
  \psplot{0}{720}{8 2.5 x mul sin mul}
\end{pspicture}

\end{document}
