Graphing Polar Equations on a Polar Plane

In the first lesson of this unit, you were lightly introduced to graphing polar coordinates. This lesson revisits what you learned earlier, and extends those ideas to graphing polar equations.

In the first of three videos below, you will learn how to graph polar coordinates with negative values, namely when:

  • the angle is negative
  • the radius is negative
  • both properties are negative

You’ll discover that when the angle is negative angle, the terminal side moves clockwise from the polar axis, and vice versa for when its positive. In addition, a negative radius gives a direction of the terminal side opposite to the angle.

Perhaps the greatest challenge to this section comes when graphing polar equations. Generally, graphing polar equations isn’t an easy task, and depending on your level of study, it can quite complicated when taking into account symmetry. Luckily, our analyse won’t exceed what we already know about negative/positive angles and radii. Starting with the first video, you’ll graph two trigonometric equations – one that’s in degrees and the other that’s in radians. To find the polar coordinates of an equation, you’ll create a table of values using angles from θ = 0° to 360°. Recall that a point with a radius of (−r) is plotted in the opposite direction to (+r).

Sometimes a polar equation can be written as a pair of parametric rectangular equations. If you encounter a question like that, one major thing to keep in mind is to follow the previous point when connecting to form your curve.