This demo includes two graphical display windows.

One window displays the graph of X(t) (which you can alter in the appropriately labeled textbox), the point X(t0), and the unit tangent vector T(t0) with base X(t0).

The other window displays the unit tangent vector T(t0) with its base at the origin and the unit circle on which the head of T(t0) must lie.

The control window lists various functions and parameters used in defining those functions. To use one of those functions as X(t), type the function name in the X(t) textbox (e.g., type "cardioid(t)" to make X(t) a cardioid).

To change t0 or any of the parameters used in defining the functions, use the following buttons in the control window:

[<]: Decrease variable by one step.
[>]: Increase variable by one step.
[<<]: Decrease variable until it reaches its minimum value.
[>>]: Increase variable until it reaches its maximum value.

By default, the demo shows the point tracing out the curve, so that only part of it is shown. To show the entire curve, check the box "Show entire curve" by clicking on it. Click on the "Show position vector X(t0)" box to show the position vector X(t0) whose components are the coordinates of the point X(t0).