# Pre-Calculus Polar Graph Project

### Christen Tamisin and Vincent Vuong

Period: 1

Our design depicts a kaleidoscope. Usually, A kaleidoscope is cylinder with mirrors containing objects such as beads, and some glass. In our kaleidoscope there are 5 graphs. The first graph (r=6cos6θ) represents a rose with polar axis symmetry, θ=π/2, and pole symmetry. The second graph (r=8sin6θ) represents a rose with polar axis symmetry, θ=π/2, and pole symmetry. The second graph is much similar with the first graph but the length is shorter by 2. The third graph (r^2=100cos2θ) represents a lemniscate with polar axis symmetry, θ=π/2, and pole symmetry. The fourth graph (r=10sinθ) represents a circle in the first and second quadrant with respect to θ=π/2 symmetry. The fifth graph (r=-10sinθ) represents a circle in the third and fourth quadrant with respect to θ=π/2 symmetry. At first we had 4 circles and two roses. Upon hearing that we needed 3 different types of polar graphs, we changed our 2 cosine circles to one lemniscate. The equations went from being r=10costheta r=-10costheta to r^2=100cos2theta.

# Phase 4

We experimented mathematically when we tried matching equations to our design while meeting the design criteria. For example, we changed graph #3 from two circles to become one leminscate to meet the design criteria. Originally we put r=-10costheta and 10costheta then we changed it into r^2=100cos2theta. Hence we experimented mathematically.

While we were completing this assignment we learnt to set enough time to do our work and how to graph polar equations more. It was hard to find time in our schedule to work on the project but to get a good grade we figured out how to manage our time. While doing the project we also learnt how to manipulate polar graphs. Therefore, we learnt managing our time was the key to finishing our polar graphs.

Yes we did enjoy working on this assignment. It was fun working with each other. Furthermore, seeing how the design progress through each phase was rewarding. Designing, matching equations, and changing the polar graphs allowed us to help understand this topic better.