Objectives: In this tutorial, we define parametric equations in the plane. We illustrate how to draw the graph of parametric equations. After working through these materials, the student should be able

• to graph a system of parametric equations.

Modules:

Definition. Parametric Equations in the plane is a pair of functions x = f(t) and y = g(t) which describe the x and y coordinates of the graph of some curve in the plane.

• Examples.

  • x = t²
    y = t² - 4t
    Discussion [Using Flash]

  • x = 3 sin(t)
    y = 5 cos(t)
    LiveMath notebook

  • x = t + 2 cos(2t)
    y = t + 3 sin(3t)
    LiveMath notebook

  • x = sin²(t)
    y = cos(t)
    LiveMath notebook

  • Animation of the drawing of the cycloid.
    Derivation of the equations of the cycloid [Using Flash]

  • x = (a + cos(3t)) cos(t)
    y = (a + cos(3t)) sin(t)
    LiveMath notebook

• Using a graphing calculator to graph a system of parametric equations:
  • TI-86 Graphing Calculator [Using Flash]
  • TI-85 Graphing Calculator