Polar Equations

by

Hyeshin Choi

Investigate

I set a=1 and b=1. Since k represents the number of this flower I set k= first. Then I have five leaf-flower.

Then I set c=3. That gives me three leaf- flower.

Now I want to try non integer for k such as k=2/7.

Since c in not an integer, the leaf of flower does not meet at a same point. So I want to change the period from 0 to 4pi.Then I have 2- seven leaf flowers. One is big and the other is inside the big flower.

Now I want to compare this graph with sin graph. So I put sin instead of cosine.Then I have same flower but it is rotated little bit to the counterclockwise.

Now I want to investigate sin graph with noninteger k which is 7/2.Then the graph doesn't look like a flower any longer.

So I changed the period from o to 4 pi.Then I got same flower picture as cos.