Question Details

MATH 142 Module 9 Discussion: The Parametric Curve
Discussion:
The parametric curve defined by  or cycloids and why they are famous.
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 sure to attribute your source(s).
•	Post your initial submission to the discussion no later than Day 5 of the module's week. If the initial submission is made during Days 6 or 7, an academic penalty is applied, but not a severe one.
•	During the week, preferably Days 6 or 7, read all the initial submissions posted by your peers. Note that this part of the exercise is like touring an art exhibit. Perusing before Day 6 means you will likely miss some excellent initial submissions that make the Day 5 deadline.
•	Post meaningful comments on at least two of them. Keep in mind that your responses in the discussion are graded as strictly as your initial submission. No “me, too” follow-ups.
•	Compliment the contributors whose submissions interested you the most. Tell them why their submission impressed you. (No one- score will be influenced by the number of compliments).