# Parametric Equations

GnuPlot includes support for Parametric Equations. To switch to parametric mode, type the following:
• set parametric
To go back to standard Cartesian mode, type:
• set noparametric
For example, to see the plot of the set of equations x = 5 cos t and y = 2 sin t, you could type the following:
• set parametric
• set xrange [-6:6]
• set yrange [-6:6]
• set trange[0:10]
• set isosamples 60
• plot 5*cos(t), 2*sin(t)

The xrange and yrange values specify the range of the graph displayed. The set trange command sets the range that is used to compute the parametric equations. If you use brackets to set a range within the plot command, it will refer to the trange. The first part of the plot command before the comma is the x equation, and the second part is the y equation.
For another example, consider trying to plot the cycloid x = t - sin t and y = 1 - cos t.

• set xrange [0:40]
• set yrange[-1:3]
• set trange [0:40]
• plot t-sin(t), 1-cos(t)

# 3D Parametric Plots

Gnuplot also supports 3D parametric plots. It uses the the variables u and v. 3D paramettric plots use the xrange, yrange, and zrange values to determine what is displayed on the screen. The urange and vrange variables can be changed to determine how much of the graph is drawn. For example,:
• set xrange [0:30]
• set yrange [0:30]
• set zrange [0:80]
• set grid
• splot 2*u, u**2 + v, v**2

If you changed the urange and vrange parameters, you would get a differant graph.

• set vrange [-10:10] - this makes the graph taller
• set urange [-7:7] - this makes the graph extend further
• set isosamples 80
• replot

Many of the standard 3D features apply to 3D parameter plots (you can use isosamples, views, and hidden3d).