Polar coordinates in the plane

A point of the plane can be located not only by the Cartesian pair $(x,y)$, but also by the polar pair $(\rho,\theta)$: the distance from the pole and the angle with the polar axis. Polar coordinates are particularly convenient when the problem has central symmetry, and they are the natural language of curves such as cardioids and spirals and, later on, of complex numbers.

• What polar coordinates are
• Conversion between polar and Cartesian
• Two languages for the same point
• Equations in polar coordinates
• Polar coordinates and complex numbers