# The Parametric Curve Defined

## The Parametric Curve Defined

DIRECTIONS:

This essay/comments about each of your graphic submissions should be focused on the parametric curve defined by x(t) = A cos(Bt), y(t) = C sin(Dt), or cycloids and why they are famous.

This assignment isof your own design but 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 a 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..

The deliverable:

•This is not a term paper, however, good-quality graphs created by your software is essential. They certainly need not be in color (to save on file size), but that is up to you. Your equations should be prepared in the Microsoft equation editor. If you found ideas for some of your pictures in some book or at some website, be sure to attribute your source(s). Please make sure that each graph created via your software is followed by a summary as stated in the above directions. Please make sure the assignment is written in the U.S. English language and uses the correct U.S. English grammar. Also, the assignment needs to follow the APA 6th edition format. If you need any additional pages to complete this assignment, please let me know.

Thank You!