Since this is the last discussion activity in this course

| August 30, 2017

The parametric curve defined by
why they are famous.

or cycloids and

Since this is the last discussion activity in this course, it should have something to do with the
trig functions sine and cosine, and with parametric equations. You’d want x to be tied to the
cosine function, while y should have something to do with the sine function. However, note that
the amplitudes need not be the same (which will produce something perhaps elliptical but at least
elongated in one direction or another), and the frequencies need not be the same. This is where
the graphs can become interesting. Your graphing tool becomes essential for this activity. Here is
a hint for this activity…think about the amplitude ratios A/C and the frequency ratios B/D in
characterizing your graphs.
Your task:
Create an initial submission in Microsoft Word, using your equation editor and graphing tool (Microsoft
Mathematics 4.0, which can plot parametric graphs, or another tool such as the shareware Graphmatica
2.0) to post interesting variations on the parametric equations. For each graph you create, identify the
specific parametric equations used and the domain for your graph. In a sense, this will be a real art
exhibit. Be sure to make a comment on each graph you create as to how one particular graph differs
from the other, and perhaps what patterns you observed during your experimentation. Heads-up, be
careful about file size. The images could get large, especially if you include color in the graphs’
backgrounds. Tradeoffs are part of the issues in this submission.

The deliverable:

This is not a term paper, however, good-quality graphs created by software or your TI
whatever is essential. They certainly need not be in color (to save on file size). Your
equations should be prepared in your equation editor. If you found ideas for some of your
pictures in some book or at some website, be su

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