## EMAT 6680 Assignment #11

## Polar Equations

#### By Kent Wiginton

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=1For n=2

For n=3For 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.

**Return**