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.
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Angular coordinates are essential in expressing points in polar coordinates.
The angular coordinate $\theta$ determines the direction of a point from the origin.
Angular coordinates can be positive or negative: counterclockwise measurements are positive and clockwise measurements are negative.
In parametric equations, angular coordinates often describe circular or spiral motions.
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.