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.

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: