
All images on this site are
graphs of two types of polar trig equations, graphed in the polar coordinate
system. This system is similar to the common (x, y) system (Cartesian axes) in
which the xaxis is the horizontal axis and the yaxis is the vertical axis.
The polar system is different in that (x, y) is replaced by (r, q ), where q (theta) is in radians, not degrees.
Theta is an angular measurement, and r is the distance from the center of a
circle.
The two types of graphs featured
on this web site are the sine and cosine. On the xy axis, these functions (sin q , cos
q )
would appear as the familiar sine wave and cosine wave. However, in the polar
coordinate system, sin q and cos q a each
form circles.
The images on this web site were
created using the following equipment:
A
TI83 calculator
A
TI83 Windows NT program, able to capture and save calculator images as bitmap
files.
A
computer
Link
cable with port attachment to link calculator with computer
It took approximately 3.5 hours
to create and upload the images, and to finally piece it all together into an
informative web site. Full conclusions have not been drawn yet about the great
significance of the trig graphs displayed here; that will be done soon.
Last year during my Precalculus
class at NCSSM, I was experimenting with the Mode button on my TI83 after I
finished my assignment for the lab period. It dawned on me that my calculator
was able to do polar equations, but since I did not know much about polar
equations other than they involved trigonometric ratios, I decided to
investigate.
I had never seen graphs like
those generated by sines and cosines on a polar coordinate system before. Upon
first viewing them, I was struck by their intricate complexity.
My initial investigation,
coupled with future knowledge of web site creation and a bit of helpful
computer technology, led to the creation of this site. This site may be the
only web site to focus on the art of polar trig graphs; if you find another web
site, please tell me!
This site is intended to be a
math resource. If you want to use any of these images for personal or
instructional use, read this section. You may use these images as backgrounds,
screensavers, clip art for presentations or research papers, and alter them in
any way you wish, with the following exceptions:
Students in NCSSM math classes: it would be educational to first learn
how to generate these images yourself, using the materials listed above.
Students in other math classes: If you absolutely do not have access and
cannot get access to all the materials listed above, you may use these images.
I don't know if this web site is
a citable source for research papers; you may want to ask your instructors
about this.
Note that one of the pleasing
things about math and art is the selfconfidence one gains when successfully
completing any project involving math or art. If you copy portions of this web
site into your work without first giving some thought to how you could go about
doing your work independently and with your resources, you will be depriving
yourself of that wonderful feeling of selfachievement. Sure, it's easy to copy
stuff off this web site, and I'm allowing you to, but make sure you've at least
thought about your problem or research first.
If you have any questions about
the material on this web site, comments, or suggestions on how to improve my
web site, please email me at clarkdbc@hotmail.com.
NC School of Science and Math
1999