Assignment 11

POLAR EQUATIONS

In this investigation, we will look at the equation r = a + bcos(kx).

In this graph, a and b both equal 1 and k is the integer 1. This is one version of the n-leaf rose. Let's now compare this to

r = bcos(kx).

Purple:

Red:

Notice that when the a is 0, we have a circle with center (.5,0) and rdius .5.

It is interesting to see what will happen when we replace cosine with sine.

Purple:

Red:

Notice that the graph has the same characteristics, it just rotates around the origin.

Now we will see what happens when a,b,c, and k are varied.

In this graph, k was increased to a value of 2. Everything else remained the same. This resulted in the graph splitting into two loops.

For k = 3:

This results in three loops.

For k=4:

This results in 4 loops.

What if a and b remain equal, but they both increase? Click here to check it out.

Next I will investigate quite a few different equations.

**Notice that this changes the size of the graphs and there is no loop.

**Notice that this changes the size of the graph.

Now I will look at .

This first graph shows when a,b,c, and k are 1.

Now I will let a and b vary at the same rate.

Now I will let c vary.

Now I will let k vary.