Investigate

* When a and b are equal, and k is an integer, this is one textbook version of the "n-leaf rose."

* Compare with

for various k. What if... cos( ) is replaced with sin ( )?

First, consider the case when fixed a and k, say a=1, k=1, i.e. .

　

　

　

　

Next, explore a graph when b=k=1 but a is changing; that is, .

　

 

　

　

　

Finally, observe the graph when a=b=1 and 'k' is changing; that is, .

 

 As k is growing, the number of leaves in the graph is increasing.

　

　

Now, replace cos ( ) by sin ( ).

When a=k=1,

When b=k=1,

　

When a=b=1,

　

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