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Rectangular Form (Coordinates)
the distance from the origin to a point
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
r = a ± b sin θ
Limaçons with inner loop
a < b in
Limaçons Cardioid (heart-shaped)
a = b in
a > b in
a ≥ 2b in
r = a sin nθ
r = a cos 2θ
r = a cos 4θ
r = a cos 5θ
r² = a² sin 2θ
r² = a² cos 2θ
The point in a polar coordinate system used as a reference. Analogous to the origin in a Cartesian coordinate system.
Number that describes a population