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Sketching Parametric Equations

What is a parametric equation?

A parametric equation is one in which a few quantities are expressed as a function of a parameter.

This is an example of a parametric equation:

y = cos t; x= sin t

In the above example of a parametric equation, notice that both x and y are expressed as a function of a parameter, t.

How to sketch parametric equation with the graphic calculator (Ti 84)

  • Press [mode]
  • Look for the row that has func par
  • pol seq, select par (default is func)
  • Press [y=], notice that now you’ll get to input functions of x and y (instead of just y)
  • input the equations
  • Go to windows, and ensure that the range of T matches the range of the parameter
  • press [graph]

Example of how to sketch a parametric equation using Ti84 graphic calculator.

Example: Sketch the graph y = cos t, x = sin t, 0≤t≤ π

  • This is in radian mode, ensure that the calculator is in radian mode
  • Also, set the calculator to par mode (instead of the default func mode)
  • Go to [y=] and type in the equations:
Type in the equation of the parametric equations into Ti84 graphic calculator to sketch the parametric equation.
  • Go to windows and set the range of t to that given. Since 0≤t≤ π, Tmin = 0 and Tmax = π.
Change the range of T in the graphic calculator for the parametric equation.
  • Press [graph]
Sketch of parametric equation on the graphic calculator Ti84.
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