Polar Equations Precalc

r = A

r = A

Circle along origin, A = radius

r = Asinθ

Circle along y-axis, A = radius

r = Acosθ

Circle along x-axis, A = radius

r = AsinBθ

Rose curve spaced throughout 360, A = radius, B = # petals

r = AcosBθ

Rose curve spaced along axis A = radius, B = # petals

Rose curve with even B

# petals = 2B, 180 degrees for full graph

Rose curve with odd B

# petals = B, 360 degrees for full graph

Loop Limacon

A / B < 1

Cardioid

A / B = 1

Dimpled Limacon (worse heart)

1 < A / B < 2

Convex Limacon (oval)

A / B >= 2

r = A ± Bcosθ

Limacon curve, a = y-int, rmax = furthest x

r = A ± Bsinθ

Limacon curve, a = x-int, rmax = furthest y

A in limacon curve (r = A ± Bsinθ)

A = (Rmax + Rmin) / 2

B in limacon curve (r = A ± Bsinθ)

B = (Rmax - Rmin) / 2

r² = A²sin2θ

Leminscate equation, A = radius, rotated 45/45

r² = A²cos2θ

Leminscate equation, A = radius, along x-axis

r = Aθ

Archimedes spiral

R = A / θ

Reciprocal spiral