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(r, θ)

polar coordinates

(x, y)

Rectangular Form (Coordinates)

r is...

the distance from the origin to a point

θ is...

the angle between the polar axis

x = r cos θ

To change from POLAR to RECTANGULAR, you use...

r² = x² + y²

To change from RECTANGULAR to POLAR, you use...

x = ? is a vertical line

If only ONE variable in rectangular is found x or y...

If no angle of θ is determined...

the graph is a circle. The "r" value found is the radius of the circle.

r = a

Polar Curves: Circle - centered at pole

r = a sin Θ

Polar Curves: Circle - shifted along the y-axis

r = a cos Θ

Polar Curves: Circle - shifted along the x-axis

Polar Curves: Spiral

r = aθ

Limaçons

r = a ± b sin θ

Limaçons with inner loop

a < b in

Limaçons Cardioid (heart-shaped)

a = b in

Dimpled Limaçon

a > b in

Convex Limaçons

a ≥ 2b in

roses

r = a sin nθ

4-Leaved Roses

r = a cos 2θ

8-Leaved Roses

r = a cos 4θ

5-Leaved Roses

r = a cos 5θ

Figure-eight-shaped curves

r² = a² sin 2θ

Figure-eight-shaped curves

r² = a² cos 2θ

Pole

The point in a polar coordinate system used as a reference. Analogous to the origin in a Cartesian coordinate system.

parameter

Number that describes a population