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r = a
circle with radius a centered at the origin

r = asin(θ)
circle with diameter a on y axis

r = acos(θ)
circle with diameter a on x axis

r = aθ
spiral

r = a ± bsinθ (a < b)
limacon with inner loop on y axis

r = a ± bcosθ (a < b)
limacon with inner loop on x axis

r = a ± bsinθ (a = b)
cardioid on y axis

r = a ± bcosθ (a = b)
cardioid on x axis

r = a ± bsinθ (a > b)
dimpled or convex limacon on y axis

r = a ± bcosθ (a > b)
dimpled or convex limacon on x axis

r = asin(nθ) (n is odd)
n leaved rose with first leaf off x axis and leaf length of a

r = acos(nθ) (n is odd)
n leaved rose with first leaf on x axis and leaf length of a

r = asin(nθ) (n is even)
2n leaved rose with first leaf off x axis and leaf length of a

r = acos(nθ) (n is even)
2n leaved rose with first leaf on x axis and leaf length of a

r² = a²sin(2θ)
lemniscate with loops in Q1 and Q3

r² = -a²sin(2θ)
lemniscate with loops in Q2 and Q4

r² = a²cos(2θ)
lemniscate with loops on x axis
