**Iwant to investigate what happens
to the graph of**

**for when a=b, a=0 and b varies,
and replacing cos with sin.**

**Let's look at the graph of the
function when a = b =1 and k =1**

**This is a graph of r = 1+ cos
t.**

**Looking at the graphs of when
a = b=1 and k varies. Therefore k is the variable under observation.
Looking at the graphs we see a strange happening that I want to
generalize below:**

As k vaires, the graph of r = 1 +cos Kt changes too. The graph takes on the form of what is called a leaf-rose graph. the number of leaves in these graphs is equivalent to k. Therefore if we set k = 7 then there will be seven leaves.

**I wonder what would happen if
I were to replace cos () with sin (). I want to graph the equation
r= b sin kt. The purposes of having only one variable in the equation,
I will set b = k = 1.**

**What about when b=k =2.**

**I do not see any obvious patterns forming yet. Do you?**