**How to use**

- Enter functions
*f* (*t*),
*g*(*t*), and
*h*(*t*)
in the text input fields
marked "*f* (*t*)=",
"*g*(*t*)=", and
"*h*(*t*)=".

(Example:
*f* (*t*)=3cos *t*,
*g*(*t*)=3sin *t*,
*h*(*t*)=*t*/3)
- Click the "Graph" button
(this button also refreshes the graph).
- Rotate the graph by
clicking and dragging the mouse on the graph.
- Enter first derivative functions
*f* '(*t*),
*g*'(*t*), and
*h*'(*t*)
in the text input fields
marked "*f* '(*t*)=", "*g*'(*t*)=",
and "*h*'(*t*)=", and click the "Graph"
button to refresh the graph.
(Example:
*f* '(*t*)=-3sin *t*,
*g*'(*t*)=3cos *t*,
*h*'(*t*)=1/3)

**Examples**

Helix:
*f* (*t*)=3cos *t*,
*g*(*t*)=3sin *t*,
*h*(*t*)=*t*/3, with
appropriate derivatives

Wavy circle:
*f* (*t*)=3cos(*t*),
*g*(*t*)=3sin(*t*),
*h*(*t*)=sin(2*t*), with appropriate derivatives

**Other Notes**

The parametric path itself is shown in blue.
The velocity vector
*v*(*t*)=<*f* '(*t*),
*g*'(*t*), *h*'(*t*)>
and acceleration vector
*a*(*t*)=<*f* ''(*t*),
*g*''(*t*), *h*''(*t*)>
are shown in orange.
The standard unit tangent vector *T* is defined to be the unit
vector in the direction of the velocity vector *v*(*t*).
The standard unit normal vector *N* is defined to be the unit
vector for which the acceleration vector *a*(*t*) lies
in the *T*-*N* plane, with component *a*_{N}
(the length of the projection of *a*(*t*) onto *N*)
being positive.
The standard unit binormal vector *B* is defined so that
*B*=*T*x*N*.
The unit vectors *T*, *N*, and *B* are shown in
green.
Labels show the values of *a*_{T} (the tangent component
of *a*(*t*)) and *a*_{N} (the normal component
of *a*(*t*)).