polar coordinate
Noun: A system for locating a point in a plane using two numbers: 1. Radial Distance (r): The distance from a fixed central point, called the pole (analogous to the origin in Cartesian coordinates). 2. Angular Coordinate (θ): The angle measured from a fixed reference direction, typically the positive x-axis.
Polar coordinates are used to represent the position of a point, especially where relationships are naturally expressed in terms of distance and direction from a center. - The location of the ship was plotted using polar coordinates, with the lighthouse as the pole. - To graph the spiral, it is easier to use the equation in polar coordinates. - The point is defined by the polar coordinate (5, π/3), meaning a distance of 5 units at an angle of 60 degrees.
- Multiple Representations: A single point can have multiple representations in polar coordinates. For example, the coordinates (r, θ), (-r, θ+π), and (r, θ+2πk) for any integer all represent the same point.
- Conversion to Cartesian Coordinates: A point given in polar coordinates (r, θ) can be converted to Cartesian coordinates (x, y) using the formulas: and .
- Polar Equations: Many curves have simpler equations in polar form (e.g., for a circle, for an Archimedean spiral).
- Polar Axis: The fixed reference line from which the angle θ is measured, analogous to the positive x-axis.
- Pole: The fixed central point (origin) in a polar coordinate system.
- Radial Coordinate: Another term for the distance from the pole.
- Angular Coordinate: Another term for the angle .
- Cylindrical Coordinates: A three-dimensional extension of polar coordinates, adding a height (z) component.
- Spherical Coordinates: A three-dimensional coordinate system using distance and two angles.
- None that are direct, single-word synonyms. It is a specific technical term. Descriptive phrases include "distance-angle coordinate system."
- Plot in polar coordinates: To graph or mark a point using its (r, θ) values.
- Convert to polar coordinates: To transform Cartesian (x, y) coordinates into their polar (r, θ) equivalent.
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either of two values that locate a point on a plane by its distance from a fixed pole and its angle from a fixed line passing through the pole
