Shapes on Polar Graphs

Class was quite the doozy today in Mathland. So many shapes yet so little times. Sometimes I feel like Miss V doesn't understand that I am a senior and academics do not appeal to me as a form of interest at this moment of my life. Im jk. Miss V is a visionary but it would be nice to not have to do school at this point. Oh well. I will go pout to my mom now. Anyways. Some of the equations and shapes we learned in class on this special day include limaçons, rose curves, circles, and lemniscates.

Limaçons:

r = a ± b cosθ
r = a ± b sinθ
(0 < a, 0 < b)

Rose curves (if n is odd, there will be n "petals"; if n is even, there will be 2n "petals"):

r = a cos(nθ)
r = a sin(nθ)
(n ≥ 2)

Circles:

r = a cosθ
r = a sinθ

Lemniscates:

r² = a² sin(2θ)
r² = a² cos(2θ)
r = a ± b sinθ
(0 < a, 0 < b)

Rose curves (if n is odd, there will be n "petals"; if n is even, there will be 2n "petals"):

r = a cos(nθ)
r = a sin(nθ)
(n ≥ 2)

Circles:

r = a cosθ
r = a sinθ

Lemniscates:

r² = a² sin(2θ)
r² = a² cos(2θ)