# Pre Calculus Polar Graph Project

### Kelsey Cha, Justin KimPeriod 1

From phase 1 to phase 2, we added a circle (r=6) to add some more creativity and depth to our design. We kept all the other equations the same because we felt like the equations creatively depicted what we wanted it to. We wanted the graph to look like a flower on a lily pad. The equations r=3cos2theta, r^2=6sin2theta, and r^2=-6sin2theta are supposed to portray the flower part in our design. We made them different lengths to add creativity into the design. The circles r=8 and r=6 are meant to portray the lily pads. Lily pads are known to be circular and that’s why we chose the equations r=8 and r=6. For phase 2, we added the equation r=6 to make the design more intricate. #polarproject1

Phase 4: In order to complete this project, my partner and I had to experiment mathematically with different types of equations in order to get the correct shape we wanted. For example, we originally thought we could use a rose curve with 3 roses, but we found out it didn't get the design we wanted, so we changed it to an equation with 4 roses. In order to get the shape and design that we desired, we had to experiment with which equations would get the designs we wanted. Mathematically we changed the numbers in the equations until we finally got the shapes that we wanted and the size we wanted it to be.

While we were completing this assignment we learned that the equations you originally planned don’t always work out. We had to continue to experiment until we liked the design and the equations all worked. We thought the equations we did at first would work out, but we learned that sometimes you have to experiment to get the correct result.

Overall, we enjoyed working on this project because it allowed us to help each other more thoroughly understand the math concepts we learned in this chapter. It also was a fun project to complete because we could see the design we had in mind come to life through rose curves, circles, and lemniscates.