key term - Pole

Definition

In polar coordinates, the pole is the origin or reference point from which the radial distance is measured. It serves as the starting point for defining the position of points in a plane using polar coordinates.

5 Must Know Facts For Your Next Test

1. The pole corresponds to $(0, 0)$ in Cartesian coordinates.
2. All angles in polar coordinates are measured from the pole.
3. A point at the pole has a radial coordinate $r = 0$ regardless of the angle $\theta$.
4. Polar equations often describe curves that pass through or are centered around the pole.
5. Transforming between Cartesian and polar coordinates requires referencing distances and angles from the pole.

Review Questions

Related terms

Radial Coordinate:

$r$, representing the distance from the pole to a given point in polar coordinates.

Angular Coordinate:

$\theta$, representing the angle measured counterclockwise from a fixed direction (usually the positive x-axis) to a given point in polar coordinates.

Polar Equation: An equation that defines a relationship between $r$ and $\theta$, describing curves or shapes with respect to the pole.