Question

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

$r=4-2\cos \theta$

Short answer

$r=4-2\cos \theta$

Step-by-step solution

Step 1. The given information is

$r=4-2\cos \theta$

Step 2. Replace θ by -θ

$$\begin{gathered} r=4-2\cos \left(-\theta \right) \\ r=4-2\cos \theta \end{gathered}$$

Test is satisfied, graph is symmetric with respect to polar axis.

Step 3. Replace θ by π-θ

$$\begin{gathered} r=4-2\cos \left(\pi -\theta \right) \\ r=4+2\cos \theta \end{gathered}$$

Graph may or may not be symmetric with

$\theta =\frac{\pi }{2}$

Step 4. Replace r by -r

$$\begin{gathered} r=4-2\cos \theta \\ -r=4-2\cos \theta \\ r=-4+2\cos \theta \end{gathered}$$

Graph may or may not be symmetric with respect to pole

Making the graph we get