Paula Whitmire

Polar Equations

Assignment 11

Let a=b and k=2

(purple)

(red)

(blue)

Notice that they all have 2 "leaves" and that the intercepts are 0, 2a, and -2a. Now we will let k=1 and a and b will remain the same as above.

 

Now we see that there is one leaf. We notice that the graph with a negative value for a=b is pointing to the left.

Now examine the same three equations with k=6.

All graphs have 6 leaves.

 

Now let us compare these with

(red)

(blue)

 

The red graph has 4 leaves or 2k and the blue graph has 2k=20 leaves.

Next we will look at k= 3 and 7.

(red)

(blue)

We notice that when k = an odd number, then the graph will have k number of leaves, and when k= an even number the graph will have 2k number of leaves.

Now we will replace cosine with sine. We notice a shift of 90 degrees.

These are FUN!!

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