Polar form

The polar form is based on polar coordinates, which you may or may not be used to. If not, the next section goes through these, otherwise, you can skip it. Also, the rest of the chapter is heavy on trigonometry and we use radians for all angles. If you require a quick refresher on these, please consult the Appendix.

Polar coordinates

Polar coordinates are another way of representing points in ℝ2. We are very familiar with the Cartesian coordinate system and its points, such as (x,y). Now we will represent a point with two coordinates called r and θ. The following diagram is very helpful in terms of putting this all together:

Figure 6.6 – Polar coordinates on a graph

As you can see, r is the hypotenuse of a right triangle with the other two sides being the Cartesian coordinates x and y. Because of this, it is easy to derive the equation to find r given the Cartesian coordinates using the Pythagorean theorem:

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