# Checkered Rose

### Viviana Ruiz, Rozele dePadua

The changes Viviana and I made to this graph is the equation and sketch for the lemniscate. Originally, it was r^2=81sin2 theta. We graphed it to have theta= pi/2 symmetry. Then, we realized that there is no such thing as a lemniscate with sin to have theta= pi/2 symmetry. Due to that fact, we decided to change the equation to r^2=64cos2 theta.

Since lemniscates cannot be graphed on desmos, we decided to change it to a cardioid. The equation is: r=3+3cos theta. We wanted our design to have more complexity. We changed the equation of the circle to r=7sin theta. Also, Viviana and I added 2 more graphs; those of which are another circle and cardioid. The equation of the circle is: r=-7sin theta and the equation of the other cardioid is: r=3-3cos theta.

We experimented mathematically when we were establishing the equations for the graphs of our design. We both felt that it would have a better appearance if we included a rose, two cardiods, and two circles to create complexity. At the beginning of this assignment, we tried to include a lemniscate that was going to be on the y-axis until we later realized that it would be mathematically impossible. We were going to then change the lemniscate from sine to cosine, but, we again realized that it would not graph on the Desmos. So, finally, we decided to include a cardiod limacon in our graph and it ended up as a success for the complex look we were hoping to accomplish and it also helped us practice more with the limacon graphs.

While completing this assignment, we were able to practice graphing cardiods, a rose, and circles. Before starting this assignment, we were unsure about the concepts for graphing the four different types of limacons. We were having difficulty and were not sure how to differentiate between the limacon graphs, but, after working on this assignment, it helped us not only how to better identify a cardiod graph, but, also, to write the equation that goes along with it. Going into this assignment, we had a fair idea about how to graph and write an equation for both the rose and the circle, so this assignment aided us in practicing those two graphs better. Overall, working on this assignment helped the both of us practice for our test and it helped us understand the concept better.

We both really enjoyed working on this project because it helped the both of us comprehend which equations go with which graph. It prepared us for our test on these kinds of graphs with all the practice we got while drawing the graphs and figuring out the equations. We believe that it helped us expand our knowledge and our skill of analyzing different problems. This project taught us that teamwork is important. It also bettered the we prioritize things, which can help us in the future, especially when we are in college.