In this assignment we will explore Polar Equations using Graphing Calculator 3.0. We will be exploring the following equation:
First let's vary a and watch what happens to the graph.
Click here for an animation.
Now let's look at varing b.
Click here for an animation of the graph as b varies.
We have one more item that we want to vary. Let's watch as theta varies.
This graph is a bit more interesting than the others.
Click here to see a cool animation of theta varing.
Some textbooks call this the n-leaf rose when a and b are equal. If you notice in the animation when n is an integer it tells how many pedals there are.
For n=1
For n=2
For n=3
For n=5
Let's look at a different variation of the original graph. What if a and b were not equal and we varied theta? Let a = 0 and b stay constant and theta will vary.
Take a
look at the animation of this equation: 
.
These are just a few different variations our original equation. See what you can discover.