Parametric Equations and Graphs
A 2D parametric curve is represented by a function p(t) = [f(t), g(t)]. In this context, we call the variable t the parameter, which belongs to a domain D. You can use either our versatile parametric graphing calculator or our dedicated parametric equations grapher to plot parametric curves step-by-step, showing their construction in both Cartesian and polar coordinate systems.
Note: The parametric curve represents either the parametric equations x = f(t) y = g(t) or r = f(t) θ = g(t)
These notations for parametric equations are used based on whether you are graphing them in Cartesian or polar coordinate systems, respectively. It is customary to represent a parametric curve correspondingly as either p(t) = [x(t),y(t)] or p(t) = [r(t),θ(t)]
Cartesian & Polar Graphs of Parametric Equations
The graph of the parametric equations is simply the set of points (ordered pairs) (f(t), g(t)) for t in a domain D.
These ordered pairs can be graphed in either xy-Cartesian coordinate system or rθ-polar coordinate system.
The following figures show the graphs of some parametric curves, generated by our graphing calculator, in both Cartesian and polar coordinate systems.
The graphs of the same parametric equations shown above are also drawn with axes rotated in each coordinate system.
