Parametric Plots

A 2D parametric curve is defined by a pair of equations x = f (t), y = g(t). The curve is the set of points (f (t), g(t)), where t ranges over an interval.

$\blacktriangleright$ To plot a 2D parametric curve

The following plot shows the parametric curve defined by x = sin 2t, y = cos 3t as the parametric plot of the vector $\left[\vphantom{ \sin 2t,\cos 3t}\right.$sin 2t, cos 3t$\left.\vphantom{ \sin 2t,\cos 3t}\right]$ with 0≤t≤2π and Equal Scaling Along Each Axis.

$\blacktriangleright$ Plot 2D + Parametric

$\left(\vphantom{ \sin 2t,\cos 3t}\right.$sin 2t, cos 3t$\left.\vphantom{ \sin 2t,\cos 3t}\right)$

dtbpF2.9992in1.9995in0ptPlot You can make a parametric plot of the pair $\left(\vphantom{ f(x),x}\right.$f (x), x$\left.\vphantom{ f(x),x}\right)$ to plot the inverse function or inverse relation of a function y = f (x). For example, to plot the cube root function y = x$\scriptstyle {\frac{{1}}{{3}}}$, observe that it is the inverse function to y = x3 and do a parametric plot.

$\blacktriangleright$ Plot 2D + Parametric

$\left(\vphantom{ x^{3},x}\right.$x3, x$\left.\vphantom{ x^{3},x}\right)$dtbpFU4.3647in2.0003in0pt y = x$\scriptstyle {\frac{{1}}{{3}}}$


The inverse relation of sin x follows. You can adjust the view to get the plot of the inverse function sin-1x.

$\blacktriangleright$ Plot 2D + Parametric

$\left(\vphantom{ \sin x,x}\right.$sin x, x$\left.\vphantom{ \sin x,x}\right)$dtbpF3in2.3021in0pt