Parametric Function

Parametric Function

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When you select Parametric from the Function Type dialog, the next line contains  the general form of the function in terms of X and Y and a parameter, T.

parametrica  parametric1 

You can define this function in these ways:

  • Modify the formula and its domain directly:

parametricb  parametric2 

  • Modify the function interactively using "handles".  In the drawing window, click the function to select it.  Click and drag it and a circle appears on the curve.  This handle represents one of the variables in the equation.  You can click and drag this handle around the drawing.  Click and drag another place on the function and another moveable handle appears  if there is another variable in the equation.

This feature is a wonderful way to understand exactly how the equation represents the function.

In the example above, X=T-asin(T), Y=b-cos(T), a click and drag gives you the b handle, and lets you drag the function up and down.  Click and drag another place on the curve and you get the a handle to change the shape of the curve.

parametric3 

Notice the Variable toolbox displays the changing values as you move the handles.

  • Modify the function after it's drawn by double clicking the function tag.
  • Modify the domain of the function after it's drawn by double clicking the curve:

  parametric4