Polar Graphs

In Pre-Calculus, we've been learning about polar graphs using Desmos. We were told to use the program to create an intricate flower like design using new equations we had learned about. 

To start, I used a simple r=asin(b*theta) equation, making "a" and "b" sliders, to create a basic four petaled flower. 

Next, I played around with the values to create the picture below. I found that the "a" value made the graph bigger or smaller while the "b" value changed the number of "petals".

After learning some of the basics, I began to get creative and used multiple equations and sliders, including r=asin(b*theta) and r=acos(b*theta) and the Spiral of Archimedes (r=theta), to make an intricate flower pattern. While I chose not to use it, we also learned about Limacon graphs: r=a+bsin(theta) and r=a+bcos(theta). By only changing the "a" and "b" values slightly, I was able to drastically change the graph's pattern. So even though only a few equations were used, many different patterns were able to be made.

After the graph was actually produced, I changed the aesthetic appearance of the graph to yield the final product.