The default coordinate system for all two dimensional plotting commands is the cartesian coordinate system.  The coords option allows the user to alter this coordinate system.  The alternate choices are:  bipolar, cardioid, cassinian, elliptic, hyperbolic, invcassinian, invelliptic, logarithmic, logcosh, maxwell, parabolic, polar, rose, and tangent.

See coords for a full description of each of these coordinate systems.

All coordinate systems are also valid for parametrically defined 2-D plots with the same interpretations of the coordinate system transformations.

With most plotting commands, Cartesian axes are displayed by default, regardless of the coordinate system used.  The plots[polarplot] command displays polar axes by default. You can also obtain polar axes by adding the axiscoordinates=polar option along with the coords=polar option.

$\mathrm{plot}\left(\sin \left(x\right)\,x=0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{polar}\right)$

$\mathrm{plot}\left(\sin \left(x\right)\,x=0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{polar}\,\mathrm{axiscoordinates}=\mathrm{polar}\right)$

$\mathrm{plot}\left(\sin \,0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{bipolar}\right)$

$\mathrm{plot}\left(\ln \left(x\right)\,x=0..2\mathrm{\pi }\,\mathrm{coords}=\mathrm{elliptic}\,\mathrm{view}=\left[-4..8\,-3..1\right]\right)$