# Polar Coordinates

Polar coordinates are for locating all things circular. For example, suppose you want to draw 12 points on a circle for the hour markers on a clock. It is much much, much easier to describe their location using polar coordinates. Indeed, it is impossible to list all of the places where polar coordinates are used. All technical drawing programs use polar coordinates. Astronomy, medicine, physics, chemistry and of course engineering rely on polar coordinates and polar functions at every level. CSI (Crime Scene Investigation), GPS, navigation and surveying systems and construction all use polar coordinates. Also, polar coordinates help us in 3D. Spherical and cylindrical coordinates are based on polar coordinates.

And believe or not, you learned about polar coordinates when you were using a compass and a protractor back in grade school. We just need to connect this visual understanding with a couple of formulas and a calculator. And we will do this step-by-step, with lots of pictures and solving problems with real numbers.

Most of this book is about understanding and learning to work with polar coordinates and converting between polar and rectangular coordinates. But for those interested ? particularly engineering and math students ? we also look at some standard polar functions with wonderful shapes and names such as the cardioids that actually describe the spread of sound waves from a typical microphone. And we visually explain the calculus transformations for area, length and volume in polar coordinates. Our tactics are always the same ? understand the ideas visually and connect it to what you already know.

## An Introduction to Polar Coordinates

Polar coordinates are used in many, many fields even at an introductory level. So instructors and educators often assume that students are familiar with and give problems using polar coordinates, polar notation and polar functions without any explanation. This is extremely frustrating to students who typically have never seen nor heard of anything other than the (x,y) rectangular coordinate system.