# The Orchid

### Polar graph project: Grace Kim & Irene Lee

PHASE 3 PARAGRAPH:

We made numerous changes to our equations from our transition of phase 1 to 2 graph. We changed our equations to:

1) r=6

2) r= 6sin(theta)

3) r= -6sin(theta)

4) r= 5cos(theta)

5) r= -5cos(theta)

6) r= 6cos4(theta)

7) r= 2sin2(theta)

8) r= the square root of 9cos2(theta)

We made changes because our phase 1 graph did not have 3 different graphs (it was missing a lemniscate,) so replaced one of the equations to be a lemniscate. We changed a majority of our equations by experimenting with numbers on desmos.com.

On phase 1, our original equation for graph number 1 was r=.5, which was changed to a value of 6 in order to create a larger base for our design. We also added a lemniscate in order to have 3 different graphs, , as our number 8 graph was originally r=5sin(theta) to r= the square root of 9cos2(theta). We modified these equations to match our implied design.

Self-reflection:

a) We experienced mathematically when we plotted in different numbers in desmos. For example, we plotted in different numbers for 6cos4(theta) by replacing the 4 to 3 to observe how many petals would coordinate well with our design.

b) While we were completing this assignment, we learned that a variety of graphs can be made and that every coefficient can make a vast difference. For example, when creating a rose graph, the coefficient before the theta determines the number of petals.

3) Yes, we did enjoy making this assignment as it was fun to explore our creativity on desmos. Plugging in and experimenting with different numbers was interesting to see what results we would get.