Converting Coordinates

Pre-Calculus · Axiom Academy

EXAMPLE Converting Between Rectangular and Polar Coordinates Three worked conversions — rectangular to polar, polar to rectangular, and a quadrant III case. We will convert points back and forth between rectangular (x, y) and polar form, always taking r > 0 and : Rectangular to polar — a quadrant III point. Nice work — you converted in both directions and handled a quadrant III angle. The two formula pairs are inverses of each other. Rectangular → polar: (the distance, by the Pythagorean theorem) and , adjusted for the quadrant. Always check the quadrant. only returns angles in , so in quadrants II and III you must add to the reference angle. The same point has one rectangular name but infinitely many polar names — fixing r > 0 and pins down a single one.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.