Radial coordinate

Definition

In polar coordinates, the radial coordinate (r) measures the distance from a fixed point known as the pole to a given point in the plane. It specifies how far away the point is from the origin.

5 Must Know Facts For Your Next Test

1. The radial coordinate is always non-negative; \( r \geq 0 \).
2. In polar coordinates, a point is represented as \( (r, \theta) \), where \( r \) is the radial coordinate and \( \theta \) is the angular coordinate.
3. The radial coordinate corresponds to the magnitude of a vector in vector analysis.
4. To convert from Cartesian coordinates (x,y) to polar coordinates (r, \theta), use \( r = \sqrt{x^2 + y^2} \).
5. If \( r = 0 \), then regardless of \( \theta \), the point lies at the origin.

Review Questions

• What does the radial coordinate measure in polar coordinates?
• How do you convert Cartesian coordinates to polar coordinates for finding \( r \)?
• What happens when the radial coordinate \( r = 0 \)?

Related terms

Angular Coordinate:

The angle measured from a fixed direction, usually represented by \(\theta\), that specifies a point's direction from the origin in polar coordinates.

Polar Coordinates:

A coordinate system where each point on a plane is determined by an angle and a distance relative to a fixed center point known as the pole.

Pole:

The fixed central point in polar coordinates from which distances are measured; equivalent to the origin in Cartesian coordinates.