# Pre-Calc Polar Graphs

Corrinne Santos

Brian Baik

My partner and I tried to create a picture that was unique. We chose not to draw a flower, but instead an owl. The owl consists a variety of polar graphs. We used a circle graph to represent the head of an owl, a lemniscate graph to represent the eyes, and a rose graph to picture the nose.

a) In what ways did you experiment mathematically?

In this project, we experimented mathematically in several different ways to create our "owl". We experimented mathematically when we tried figuring out what equations we needed to use to input into Desmos in order for our design to represent an owl. We used a circle graph to represent the head of the owl and did not want our owl to look too small or too big so we came to the conclusion and graphed it at r=4. In addition, we incorporated a leminscate graph to substitute as the eyes. We had to keep changing our 'a' values to determine how big the owl's eyes would be. Lastly, we included a rose graph to add a variety of polar graphs to our overall design.

b) What did you learn from doing this project?

While we were completing this assignment, we not only learned how to graph a circle, rose, and leminscate but we also found out how to create equations for each type of polar graph. I also learned that equations are a key point in graphing different types of polar graphs. For our circle graph, we had to use the equation r=n. For our leminscate, we used r^2=acosn(deta). And for our rose graph, we used the equation r=acosn(deta).

c) Did you enjoy working on this assignment? Why or why not?

We enjoyed working on this assignment because we were able to improve our understanding of polar graphs and were able to demonstrate our abilities on how to graph different types of polar graphs. Overall, it was a fun project to do (the drawing part at least).