# Math Help - graph of a polar equation

1. ## graph of a polar equation

How do I do this?

Identify and graph the polar equation r=2+4cos (theta). Label three points.

How do ifind the points basically? Thank you

2. ## Re: graph of a polar equation

I'm assuming you want the polar plot, instead of the cartesian. Have you learned the standard forms for polar equations? This example will form a type of limaçon, specifically a cardioid with an inverted loop (I'm sure this isn't the official name, but I'm afraid my vocabulary here is lacking)

We need to know firstly where it will cut the initial line. This is where $\theta=0$, which is when $r=6$ (and this can be stated as the first point) and when $\theta =\pi$ which is when $r=-2$ (second point), however we have to be cautious with the magnitude of this measurement. Because we measured from where $\theta=\pi$, we are measuring 2 units in the positive direction.

This is really enough information to sketch the polar graph in my opinion, and as for the third point, just take a value for $\theta$ and calculate the value for r.

Using wolfram alpha gives something that looks like , which shouldn't be a surprise to you.