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How to | Plot Parametric Functions

The Wolfram Language can plot parametric functions in both two and three dimensions. Use a parametric plot when you can express the and or , , and coordinates at each point on your curve as a function of one or more parameters.

Plot the parametric curve where the parameter varies from to :

Wolfram Language code: ParametricPlot[{2 Sin[t], Cos[t]}, {t, 0, 2 Pi}]
    

You can plot two parametric curves by putting them in a list:

Wolfram Language code: ParametricPlot[{{2 Sin[t], Cos[t]}, {Sin[t], 2Cos[t]}}, {t, 0, 2 Pi}]
    

Plot more parametric curves by adding them to the list:

Wolfram Language code: ParametricPlot[{{2 Sin[t], Cos[t]}, {Sin[t], 2Cos[t]}, {Sin[t], Sin[t] Cos[t]}}, {t, 0, 2 Pi}]
    

Use ParametricPlot3D to plot the surface defined by :

Wolfram Language code: ParametricPlot3D[{r Cos[t], r Sin[t], Log[r ^ (1 / 2)]}, {r, 0.1, 1}, {t, 0, 2Pi}]
    

Plot the parametric curve in 3D:

Wolfram Language code: ParametricPlot3D[{5 Cos[u], 5 Sin[u], u + Sin[u]}, {u, -2Pi, 2Pi}]