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Level 529

Polar Coordinates & Equations


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Pole
The point in a polar coordinate system used as a reference. Analogous to the origin in a Cartesian coordinate system.
Polar Axis
A fixed ray with origin at the pole, usually horizontal, from which an angle can be established. Analogous to the x-axis in a Cartesian coordinate system.
Corresponding Polar Coordinates
A point with polar coorinates (r, θ), θ in radians, can also be represented by either:
Conversion from Polar to Rectangular Coordinates
If P is a point with polar coordinates (r,θ), the rectangular coordinates (x,y) of P are given by
Conversion from Rectangular to Polar Coordinates
If P is a point with rectangular coordinates (x,y):
Use formulas
Transforming Equations between Polar and Rectangular Forms
Polar Equation
An equation whose variables are polar coordinates.
Graph of a Polar Equation
All points whose polar coordinates satisfy a particular polar equation.
Straight Line Graphs of a Polar Equation
Let a be a nonzero real number. The graph of equation
Circle Graphs of a Polar Equation
Let a be a positive real number. Then
Cardioid
r=a+asinθ
Limaçon (no inner loop)
A polar equation of the form
Limaçon (inner loop)
A polar equation of the form
Rose Curve
A polar equation of the form
Lemniscate
r^2= a^2cos2(theta)
Logarithmic Spiral
A polar equation of the form