Question

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r=2+2\cos \theta$

Short answer

$r=2+2\cos \theta$

Step-by-step solution

Step 1. The given information is

$r=2+2\cos \theta$

Step 2. Replacing θ with -θ for polar axis 

$$\begin{gathered} r=2+2\cos \left(-\theta \right) \\ r=2+2\cos \theta \end{gathered}$$

graph is symmetric with polar axis.

Step 3. Replace θ with π-θ

$$\begin{gathered} r=2+2\cos \left(\pi -\theta \right) \\ r=2-2\cos \theta \end{gathered}$$

Graph may or may not be symmetric with$\theta =\frac{\pi }{2}$

Step 4. Replacing r with -r

$$\begin{gathered} r=2+2\cos \theta \\ -r=2+2\cos \theta \\ r=-2-2\cos \theta \end{gathered}$$

Graph may or may not be symmetric with respect to pole.

Step 5. Making the graph we get