r = 3 + 2 cosθ

r = 2 + 3 cosθ

r = 2 + 2cosθ

r = 3cosθ

Θ = π/4

Θ = -5π/4

Θ = -3π/4

Θ = 5π/4

rose

lemniscate

spiral

circle

F

E

B

A

Rose with 4 leaves, Length 4

Rose with 8 leaves, Length 4

Cardioid with length 3

Inner loop limacon with lengths 3 and 4

Circle facing up with length 3

Circle facing down with length 3

Cardioid facing up with length 3

Cardioid facing down with length 3

r² = -9sin(2θ)

r² = 9cos(2θ)

r² = -9cos(2θ)

r² = 9sin(2θ)

Circle

Cardioid

Rose with 5 leaves

Rose with 9 leaves

Spiral of Archimedes

Logarithmic Spiral

Spiral of Antiquity

Limax Spiral

r² = 9cos2θ

r² = 9sin2θ

r² = 3cosθ

r² = 3sinθ

(X, Y)

(θ, r)

(r,θ)

(Y_Y)

r = 3 + 2 cosθ

r = 2 + 3 cosθ

r = 2 + 2cosθ

r = 2 - 3cosθ

Limacon with inner loop

Limacon without inner loop

rose

spiral

Limacon with inner loop

Limacon without inner loop

rose

spiral

r = 4

r = 8

r = 4sin(Θ)

r = 8sin(Θ)

r = 4sin(Θ)

r = -2sin(Θ)

r = 2cos(Θ)

r = -4cos(Θ)

Outer Loop: 8, Inner Loop: 2

Outer Loop: 4, Inner Loop: 1

Outer Loop: 16, Inner Loop: 4

Outer Loop: 15, Inner Loop: 2

A limacon with an inner loop

A dimpled limacon

A cardiod (heart)

A circle

A limacon with an inner loop

A dimpled limacon

A cardiod (heart)

A circle

A limacon with an inner loop

A dimpled limacon

A cardiod

A line

A limacon with an inner loop

A dimpled limacon

A cardiod

A flower

Both are on the x-axis, but one faces right while the other faces left

Both are on the y-axis, but one faces up while the other faces down

One is on the x-axis while the other is on the y-axis

They are the same!

r = sin 4θ

r = 6 sin 2θ

r = 6 cos 4θ

r = cos 4θ

r = sin(7θ)

r = 7sin(2θ)

r = 2sin(7θ)

r = 2sin(14θ)

rose

lemniscate

spiral

circle

lemniscate

limacon with inner loop

cardioid

rose

Cardioid

Circle

Inner loop limacon

Rose with 6 leaves

3 leaf rose

6 leaf rose

2 leaf rose

4 leaf rose

r² = -9sin(2θ)

r² = 9cos(2θ)

r² = -9cos(2θ)

r² = 9sin(2θ)

pole, polar

radius, x

pole, x

radias, polar

$\left(4,\ \frac{7\pi}{4}\right)$

$\left(4,\ \frac{3\pi}{4}\right)$

$\left(-4,\ \frac{3\pi}{4}\right)$

$\left(-4,\ -\frac{\pi}{4}\right)$

$\left(2,\ \frac{11\pi}{12}\right)$

$\left(-2,\ \frac{13\pi}{12}\right)$

$\left(2,\ -\frac{13\pi}{12}\right)$

$\left(2,\ \frac{13\pi}{12}\right)$

$\left(5,\ -\frac{2\pi}{3}\right)$

$\left(-5,\ \frac{2\pi}{3}\right)$

$\left(5,\ \frac{2\pi}{3}\right)$

$\left(5,\ -\frac{\pi}{3}\right)$