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About TrigLife



The Polar Coordinate System


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 x-axis is the horizontal axis and the y-axis 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 x-y 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.

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The images on this web site were created using the following equipment:


A TI-83 calculator

A TI-83 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.

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Why this Site was Created


Last year during my Precalculus class at NCSSM, I was experimenting with the Mode button on my TI-83 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!

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Use of this Site


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 self-confidence 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 self-achievement. 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.

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If you have any questions about the material on this web site, comments, or suggestions on how to improve my web site, please e-mail me at


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NC School of Science and Math