Problem: Investigate

When a and b are equal, and k is an interger, this is a shape of the "n-leaf rose."

Let's look at the graph when a and b are equal, and k are various integers and the other one when a and b are the various same integers, and k is fixed.

Also, let's compare the graphs when we cosine function is replaced with sine function.
 

So, we can know that a and b just decide the size of the graph when a and b are equal.

Click here if you would enjoy the shapes of the "n-leaf rose" for various n.

Let's compare the above one with

Let's look at the graph when  b is fixed, and k is various integer and the other one when  b is  various integer,  and k is fixed.

First, let's look at the graph when b is fixed as 1, and k is various integer.
 
 

Secondly, let's look at the graph when  b is  various integer,  and k is fixed as 1.

So, we can conclude that  b is related to the radius and k is related to the period of  the graph.

And sine function change the direction of the graph.