To begin this project we plugged in a various amount of numbers into the equations of limacons, roses, lemniscates and circles. We started off with basic circles and moved on to more intricate graphs. We had trouble placing the pedals of roses, but after reviewing our notes we were able to construct both the cosine and sin rose graphs. The limacons required some additional research; however, the graphs came out the way we wanted to design them in the end. We also experimented with the lengths of the pedals so they would fit inside the circles. Also, we also had to change the sizes of the circles so the would not overlap the other graphs.
From this assignment we were able to figure out the lengths and number of pedals there are in a rose graph. We were also reminded that if there is an even number placed in front of theta the number of pedals are doubled. To remind us the placement of circles we looked at sign before cos and sin to see whether the circle would move up, down, left or right. As for the limacon we were able to figure out the different types there are. For our project, we picked the limacon with an inner loop.
We enjoyed working on this project because it prepared us for the chapter 6 test. It also allowed us to be creative in making different shapes to make a cool design. However, with all the AP tests it was very hard to keep up with the group project, notes and test. In the end, group projects are always a fun assignment and a way to raise our grades. I hope you enjoyed this project.