Angular coordinate

Definition

An angular coordinate is a measurement that specifies the angle of a point relative to a fixed direction, typically the positive x-axis. It is commonly denoted by the Greek letter $\theta$ and measured in radians or degrees.

5 Must Know Facts For Your Next Test

1. Angular coordinates are essential in expressing points in polar coordinates.
2. The angular coordinate $\theta$ determines the direction of a point from the origin.
3. Angular coordinates can be positive or negative: counterclockwise measurements are positive and clockwise measurements are negative.
4. In parametric equations, angular coordinates often describe circular or spiral motions.
5. The interval for angular coordinates is usually $0 \leq \theta < 2\pi$ radians.

Review Questions

• What does an angular coordinate measure?
• How is an angular coordinate represented in polar coordinates?
• In what units can you express an angular coordinate?

Related terms

Polar Coordinates:

A coordinate system where each point on a plane is determined by its distance from a reference point and its angle from a reference direction.

Radians: A unit of measure for angles based on the radius of a circle; one radian is the angle subtended by an arc of a circle with the same length as the radius.

$r$ (Radial Coordinate): The distance from the origin to a point in polar coordinates, representing how far away the point is from the center.