Polar Grpah

Circle

a graph that reflects where r = a

Circle (reflected across the y-axis

In polar coordinates, it represents all points equidistant from a central point, defined by the equation $r = a$sin(theta) where the circle is on the y - axis

Circle (reflected across the x-axis)

In polar coordinates, it represents all points equidistant from a central point, defined by the equation $r = a$cos(theta) where the circle is on the x - axis

Cardioid (limaçon)

cardioid is a heart-shaped curve that can be represented in polar coordinates by the equation a=b

limaçon w/ inner loop

a equation where a and b are constants, and ∣b∣>∣a∣∣ which creates the characteristic inner loop.

dimpled limaçon

r=a+bsin⁡(θ)r=a+bsin(θ), where a and b are constants and 0<∣b∣<∣a∣0<∣b∣<∣a∣. This condition results in the

four- leaved rose

where a is a positive constant that controls the size of the petals. r=acos2(theta)

three-leaved rose

where b is the positive constant three.

eight-leaved rose

where b is the positive constant is 4

five- leaved rose

where b is the constant 5

Lemniscates

r² = a²sin2(theta)

lemiscates

r²=a²cos2(theta)