The following animations offer a
comparison of polar and Cartesian graphing.
Graphing
calculators and computer software permit construction of complicated
graphs within seconds. However, one must often take a polar
equation and write it in
parametric form. If your grapher does not have a
builtin polar graphing command, then take the polar equation and write
as follows:
In GeoGebra it is easy to alter all variables and constant terms while
watching the dynamically changing curve. Finally, it is possible
to watch an animation using color.

Click on the
image
to see the
equation. 









These
curves are
created with GeoGebra, a free software that allows users to work with
Algebra, Geometry, Trigonometry, Statistics and Calculus. They
are graphs of polar functions of the form
where a, b, and c are real numbers and i, k, and m are positive
integers. Some of these graphs are not obtainable on handheld
graphing calculators with lower resolution displays. Slides 7 and
8 are rotated 90 degrees counterclockwise from the original graphs.

