This write-up will involve equations of the form: x = a cos (t) and y = b sin (t). Each section will describe what happens when the sin and cos functions are taken to different exponents and what happens when a = b, a < b, and a > b. The purpose of the explorations is to try and determind if there is any way to generalize any patterns that might arise.
The first section looks at the basic parametric equations:
Click here for a discussion.
The second section looks at equations of the form :
Click here for a discussion of section two.
The third section looks at equations of the form:
Click here for a discussion of section three.
The final section looks at conclusions and one misconception that arises based on the previous three sections.
Click here for the discussion of section four.