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).

Change the value of t0 and other variables as in earlier demos.
As in earlier demos, there are "Show entire curve", "Show position vector X(t0)" and "Show Color Spectrum" options. "Show Color Spectrum" also colors the unit tangent vector.