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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
built-in 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.
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Click on the
image
to see the
equation. |
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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 hand-held
graphing calculators with lower resolution displays. Slides 7 and
8 are rotated 90 degrees counterclockwise from the original graphs.
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