##### 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)=".

*Click* the "Graph" button.

__Example__:
*f* '(*t*)=-3sin *t*,
*g*'(*t*)=3cos *t*,
*h*'(*t*)=1/3

*Enter* second derivative functions *f* ''(*t*),
*g*''(*t*), and
*h*''(*t*)
in the text input fields
marked "f''(t)=",
"g''(t)=", and
"h''(t)=".

*Click* the "Graph" button.

__Example__:
*f* ''(*t*)=-3cos *t*,
*g*''(*t*)=-3sin 3*t*,
*h*''(*t*)=0

*Click* the "+" and
"-" buttons under the field marked
"t=" to change the position at which the
vectors are drawn on the graph. (Holding a button down causes its
action to be repeated.)

*To erase* the graph and all input fields, click the
"Clear" button.

##### Examples

__Helix__:
*f* (*t*)=3cos *t*,
*g*(*t*)=3sin *t*,
*h*(*t*)=*t*/3, with
appropriate derivatives
__Wavy circle__:
x=3cos(t), y=3sin(t), z=sin(2t), 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*)).