# 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:
• Go to windows and set the range of t to that given. Since 0≤t≤ π, Tmin = 0 and Tmax = π.
• Press [graph]
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