The Cartesian coordinate system, the one you’ve been using up to now, is not the only way to find your way around the plane. In the Cartesian system, every point has two coordinates representing its distance and direction from the y-axis and the x-axis.

In the polar coordinate system points are identified by an ordered pair by giving the direct distance, r, to the pole (the origin) and the angle measured counterwise from the polar axis (the positive x-axis) to the line from the pole to the point. The independent variable is and r is a function of .

Here is a Desmos program that will help you see how polar graphing works. Polar graphing paper shows concentric circles measuring the distance from the pole and with rays at common angles to help you locate points.

While there is a lot to be learned by studying polar curves¸ the AP Calculus BC exams are chiefly concerned with finding the area enclosed by a polar curve or between two polar curves, and the rates of change associated with a point moving along a polar curve. You will not be asked to name or know the equations of various curves (other than circles). The graphs are usually given, and your graphing calculator has a way of entering polar equations. (Be sure you learn how to do this.)

It has advantages in that some curves are much easier to write and graph in polar form than in Cartesian. In civil engineering (land surveying) it is easier to measure in the field an angle and a distance, rather than two right angles and two distances.

Changing back and forth from polar to Cartesian form is not difficult and you will learn a few formulas to accomplish this.

The polar coordinates of a point are not unique. The angle may be measured more than once around. This can be both an advantage and a disadvantage.

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Course and Exam Description Unit 9, Sections 9.7 to 9.9. This is a BC only topic.