Polar equation

Definition

A polar equation expresses the relationship between the radius $r$ and the angle $\theta$ in a polar coordinate system. It is often used to describe curves and conic sections.

5 Must Know Facts For Your Next Test

1. Polar equations use the variables $r$ (radius) and $\theta$ (angle).
2. $r = f(\theta)$ is a common form of polar equations.
3. Converting between polar and Cartesian coordinates involves $x = r \cos(\theta)$ and $y = r \sin(\theta)$.
4. Common plots include circles, spirals, roses, and lemniscates.
5. Symmetry in polar graphs can simplify analysis; for example, symmetry about the x-axis implies that for every $(r, \theta)$ there is also a point $(r, -\theta)$.

Review Questions

• What are the general forms of converting Cartesian coordinates to polar coordinates?
• Describe how you would plot a circle with radius 3 using a polar equation.
• How does symmetry help when analyzing polar graphs?

Related terms

Polar Coordinates: $$(r, \theta)$$ represent points based on distance from origin and angle from positive x-axis.

Conic Sections: Curves obtained by intersecting a plane with a double-napped cone; includes ellipses, parabolas, and hyperbolas.

Cartesian Coordinates: $(x, y)$ represent points based on horizontal and vertical distances from origin.