The parametric curves defined by r (t) A cos(Bt), y(t) C sin(Dt) define very int

Question

The parametric curves defined by r (t) A cos(Bt), y(t) C sin(Dt) define very interesting curves. In this activity, you will explore their graphs and have an opportunity to discuss why they are famous. You'd want z 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 Note: 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 graph:s. Your Task S- 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 (there should be at least three different graphs) 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. Trade offs are part of the issues in this submission The Deliverable

Explanation / Answer

Here i am providing some links as needed

Here are some good collection of parametric equation with their equation and graph for your project.

http://www.ltcconline.net/greenl/courses/107/polarparam/parameq.htm

http://www.millersville.edu/~bikenaga/calculus/parametric-equations/parametric-equations.html

to test them you can use this graphing calculater (instructions are included)

https://www.desmos.com/calculator/ksjcpazwa9

for colorful and some more complicated parametric equaitons chech this

https://www.google.co.in/search?q=parametric+equations&source=lnms&tbm=isch&sa=X&ei=VR0BVbXHDIiIuAT8kYCQAw&ved=0CAgQ_AUoAg&biw=1366&bih=657#imgdii=_&imgrc=bUZ2XraJLxODgM%253A%3BKgaBMdA8v03FRM%3Bhttps%253A%252F%252Ftheputterer.files.wordpress.com%252F2011%252F04%252Fparametricequation.png%3Bhttps%253A%252F%252Ftheputterer.wordpress.com%252F2011%252F04%252F02%252Fmac-os-x-grapher-using-parameters%252F%3B1055%3B806

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