Santa has nothing on these Polar Equations
By Stephanie Britt
Polar equations are representations of a two dimesional coordinate system where each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction.
One of the most elementary polar equations is
Now if we manipulate the values of a, b and k how will the graph change?
The most interesting equations are the teal and yellow ones. You can see that as the values of b and k differ then the leafs of the graphs are created are increase. Let's look at them seperately.
As the value of k increases we can see the number of rose petals increases.
Now let's compare them to
If you notice the pedals increased by eliminating the value of a. If we use sine instead of cosine, how much of a change will we see?
The petals of the graph when we use sine rotate from the axis to the quadrants.
Below is a movie that shows the progression of increasing petals.
It is also possible to include sine and cosine together to make overlapping petals. Can you think of any applications that you would use this for?
