### Parametric Paths (3-D Graphing)

Graphs a path in three dimensions specified parametrically, as x=f(t), y=g(t), and z=h(t), with parameter t.
How to use   ||   Examples   ||   Other Notes

How to use
• Enter functions f1(t), g1(t), and h1(t) in the text input fields marked "f1(t)=", "g1(t)=", and "h1(t)=" (Example: f1(t)=3cos 3t, g1(t)=3sin 3t, h1(t)=t)
• Click the "Graph" button (this button also refreshes the graph)
• Rotate the graph by clicking and dragging the mouse on the graph.
• To see two curves graphed simultaneously:
• Enter the second set of functions f2(t), g2(t), and h2(t) in the text input fields marked "f2(t)=", "g2(t)=", and "h2(t)="
• Click (to its "on" state) the check box next to this set of input fields
• Click the "Graph" button
(Example: f1(t)=3cos 3t, f1(t)=3sin 3t, and f1(t)=t; f2(t)=1+3t, g2(t)=2-2t, and h2(t)=3+t)
Up to 3 curves can be graphed simultaneously
• To remove a curve from the graph, click (to its "off" state) the check box next to the associated text input fields and click the "Graph" button to refresh
• To erase the graph and all input fields, click the "Clear" button
• There are two input fields which specify bounds on the variables for the function:
• The variable t takes values between tmin and tmax, specified by the fields marked "tmin=" and "tmax=".
• These two text input fields can accept any decimal number input.
The text input fields for functions can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates.
Examples
 Line: f2(t)=1+3t g2(t)=2-2t h2(t)=3+t Helix: f1(t)=3cos 3t g1(t)=3sin 3t h1(t)=t Wavy Circle: f1(t)=3cos t g1(t)=3sin t h1(t)=sin 3t Ellipses: f1(t)=3cos t g1(t)=2+5sin t h1(t)=0 f2(t)=0 g2(t)=-2+5sin t h2(t)=3cos t

Other Notes