Question

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

$r=2-\cos \theta$

Short answer

$r=2-\cos \theta$

Step-by-step solution

Step 1. Given information

$r=2-\cos \theta$

Step 2. Replace θ by -θ

$r=2-\cos \left(-\theta \right)$

$r=2-\cos \theta$

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

Step 3. Replace θ by π-θ

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

Graph may or may not be symmetric with

Step 4. Replace r by -r

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

Graph may or may not be symmetric with respect to pole

Step 5. Making the graph we get,