Assignment 11: Polar Equations

By Kendyl Wade

Let's explore the polar equation for when a = b.

for k = 7

 

The tips of the petals are 2b units away from the origin. Here you can see what happens to the graphs as k varies between 0 and 20 by increments of 1/3:

We can notice that for every value of k, there are k petals.

Now lets look at the equation .

 

for k = 4

 

The petals now go out a distance of b units from the origin. Here you can see what happens as k varies between 0 and 20 by increments of 1:

Notice that when k is odd, there are k petals, but when k is even, there are 2k petals.

To get a better idea of the relationship between (when a = b) and , let's see them on the same graph.

for k = 7

 

Here we can see what happens with values for k between 0 and 20, moving at increments of 1.

Now it's more clear that with the omission of the parameter a: the petals are 1/2 the length and when k is even, there are twice as many petals.

 

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