# Pre-Calculus Polar Graph Project

### Esther Kim, Diane Lee

phase 1 graph

phase 2 graph

Our design is simple flower. The center is created with simple circle, and petals are made by the rose graph of 8 petals. Lastly, the sepal of flower is made by two sin theta lemniscates.

While doing this project, we experimented mathematically when we self-graphed the polar graphs and had to write and equation for each of the graphs we chose. The graphs we chose are circle, rose, and lemniscate and we got to come up with our own equations for these three polar graphs to make a shape that looks like a flower. We also got to play around with the graphs to make a shape that we wanted and by doing so, we learned that many different shapes can be formed with many different polar equations. When we finally made our equations and graphed it on Desmos.com, we got our graphs to look like a flower which was very cool and fun. We also got to see the precise locations of each of the graphs we inputted which helped us to understand better about the graphs and the equations for each of the graphs.

While we were completing this assignment, we learned that it is very important to have the correct equations for each of the polar graphs. We also learned that coming up with an equation for each of the graphs takes time and the equations have to be precise and accurate in order for the graph to match the shape of the graph. Also, it is very important to know how to graph equations with sine and cosine because they are totally different from each other and it is important to know how to graph them differently. Also, along with the difference between sine and cosine graphs, there is also a difference between negative and positive equations and it is essential to graph accordingly to the signs of the equation. We learned many different things from the project but most importantly, we learned that having the correct equations and knowing how to graph them accordingly to the equations is very important.

We enjoyed working on this assignment because we got to create our own equations and got to graph many different shapes. It was fun making different graphs and trying out many different equations to create a unique shape of our own. Working on the computer and graphing on the computer was especially fun because we got to easily play around with the graphs by inserting many different equations and putting many different signs and values. By doing this project, we not only had fun making different shapes but we also learned how to write equations according to the graph and graph according to the equations. Designing and coming up with many different equations was very interesting and fun and we felt like we spent our time productively by doing this project. Also, since it was a partner project, we relied on each other for advises and we worked really hard together to complete the project which made us more closer. Overall, we had so much fun doing this project and we hope we do these kind of projects more often.