Why the formulas work

A polar point is defined by a distance rr from the origin and an angle hetaheta from the positive x-axis.

Dropping that point onto the axes creates a right triangle, so the horizontal and vertical components become rcos(heta)rcos( heta) and rsin(heta)rsin( heta).

The plane preview helps you confirm the converted point lands in the expected quadrant.

Quick usage tips

  • Keep the angle in radians unless you convert degrees first.
  • If the radius is zero, the point stays at the origin regardless of the angle.
  • Negative x or y values usually mean the point lies in quadrant II, III, or IV.