Graphs of Cosine

By Tonya C. Brooks

In this investigation, I decided to look at the graph of r = a + b cos(kq).  LetÕs look at the graph when a, b and k are all equal to 1.

This doesnÕt look very exciting to we will look at other values of a, b and k and letÕs let them all be the same for a time.

Here, you can see several different cases of when a, b and k are all equal.  What do you notice?  Do you see why this set of equations might be called an n-leaf rose?

Now, letÕs take a look at what happens when we keep a and b the same and let k differ.  Here is a collection of several cases.

Do you see any similarities from before?  How many leaves are there for the different k-values?

LetÕs look at a few others that might be interesting.

What do you notice for cases when our a is larger than our b?  How can you see this from the equation?

Take a look at the last graph.  What is happening?  Any guesses as to why this might happen?  LetÕs look a little more in depth on this case by looking at a few other graphs.