Convert Point From Polar Coordinates to Cartesian Coordinates

To convert a point from the Polar Coordinate System to Cartesian Coordinate System you can use the definition of sine and cosine to solve for the x and y component of the corresponding point. Note, the variable r corresponds with the distance from the origin to the point P and the variable θ corresponds with the angle from the positive X axis to the point.

In the example above, where P = (104, 0.98), substitute 104 for r and 0.98 radians for θ. Try dragging around the points in the interactive above to get a feel for converting different points.

Explanation

Both systems describe the position of a point in space. A point in the Polar Coordinate System is defined in terms of a radius and an angle: P = (r, θ). A point in the Cartesian Coordinate System is defined in terms of a x and y component: P = (x , y). Both define the point relative to the origin of the system. Geometrically, the two points can be described by the right triangle below.

A point in the polar or cartesian plane can be described by a right triangle.

Then, since we want to solve for the x and y coordinate in the cartesian coordinate system, we can solve for x and y in the corresponding equations:

Links

Point | concept
Radians | concept
Degrees | concept
Polar Coordinate System | concept
Cartesian Coordinate System | concept