University Mathematics Handbook (2015)

II. Functions

Chapter 4. Functions in Polar Coordinate System

A function in a polar coordinate system (see III, 1.2) is a rule expressing the distance from the origin as dependent of the variable of angle , .

Notice: must always be non-negative.

To draw the graph of that function, we can take any angle in the domain of the function, draw the appropriate ray and mark it with a point at a distance from the origin equal to .

Examples:

a.  , for all angles . Since the distance from the origin is , it is a circle of radius (Figure 1).

b.  , Archimedean Spiral (Figure 2).

c.  , a circle with radius , the center of which is at (Figure 3).

    Figure 1    Figure 2    Figure 3