Polar Coordinate System

Polar Coordinate System

The Polar Coordinate System describes points in space using an angle and radius relative to the origin. Angles are measured using radians, where a full rotation around the circle is equal to approximately 6.283 radians or τ (tau) radians. A point is denoted in the same fashion as the cartesian coordinate system. The first component represents the radius of the point, and the second component represents the angle of the point.

Point in Polar Coordinate System

Interactive Polar Coordinate System

The interactive graphic below demonstrates a point in the polar coordinate system. Click and drag the blue control point to see how its position is represented.

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Radians | Concept

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

Cartesian Coordinate System | Concept

The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system.

Convert Polar to Cartesian Coordinates | Example

To convert a point from the Polar Coordinate System to the Cartesian Coordinate System the functions sine and cosine are used to calculate the x and y component of the corresponding point.

Polar to Cartesian Coordinates | Formula

To convert a point from polar coordinates to cartesian coordinates, the trigonometric functions cosine and sine can be used.