by: Tim Lehman

Write-Up #11

For this writeup, we are studying polar cordinates. We will inspect

r=2a sin(k) +b and r=2a cos(k) for various values of a, b, and k. To start, we will vary one of the three variables a, b, and k and hold each of the other two variables constant.

We will first examine the effect on the graph by holding k at 1, b at zero, and varying a.

For an idea what this looks like, check out
**this movie**.

Next, we will hold a=1, b=0, and look at different
values for k. A movie of this graph is available **here**.

Lastly, we study the graph when a=1, k=1, and
b varies. For a graph of this when b changes from -10 to 10, **click here**.

We will first examine the effect on the graph by holding k at 1, b at zero, and varying a.

For an idea what this looks like, check out
this **movie**.

Next, we will hold a=1, b=0, and look at different
values for k. A movie of this graph is available **here**.

Lastly, we study the graph when a=1, k=1, and
b varies. For a graph of this when b changes from -10 to 10, **click here**.