Parametric Equations

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/ParametricEquations.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ParametricEquations.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

pts={Point[p={Cos[#],Sin[#]}],Text[TraditionalForm[θ==#],1.15p]}&/@{0,3Pi/2,.4,4,1.1,2Pi/3,5.5};
Show[Graphics[{
{Red,Circle[{0,0},1]},
PointSize[.02],pts
}
]]

Animation

<<Utilities`GIF`

dt=2Pi/20;
Export[gifs<>"parametr.gif",Table[Show[GraphicsArray[{
Graphics[{RGBColor[1,0,0],Line[Table[{Cos[#],Sin[#]}&@x,{x,0,t,.01}]]},Axes->True,Ticks->None,
PlotRange->{{-1,1},{-1,1}},AspectRatio->Automatic],Graphics[{RGBColor[1,0,0],Thickness[.02],Line[{{0,0},{t,0}}]},Axes->True,Ticks->{Table[{Pi/2 n,TraditionalForm[Pi/2 n]},{n,0,4}],None},AxesLabel->{TraditionalForm[HoldForm[t]],None},PlotRange->{{-.05,2Pi+.05},{-.05,.05}}]}]],
{t,0,2Pi,dt}
]]