Polar Graphs

cardioid equation (sine)

r = a(1±sin θ)

cardioid equation (cosine)

r = a(1±cos θ)

cardioid graph

1 passes through pole

limacon equation (sine)

r = a ± b sin θ

limacon equation (cosine)

r = a ± b cos θ

limacon graph (a>b)

0 passes through pole

limacon graph (a

2 passes through pole

rose curve equation (sine)

r = a sin (nθ)

rose curve equation (cosine)

r = a cos (nθ)

rose curve graph (n = 3,5,7...)

n petals

rose curve graph (n = 2,4,6...)

2n petals

lemniscate equation (sine)

r² = a² sin (2θ)

lemniscate equation (cosine)

r² = a² cos (2θ)

lemniscate graph

chopper

spiral equation

r = exp(aθ)

spiral graph

ayahuasca