Question

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

$r=2+\sin \theta$

Short answer

$r=2+\sin \theta$

Step-by-step solution

Step 1. Given information

$r=2+\sin \theta$

Step 2. Replacing θ with -θ for polar axis 

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

graph is symmetric with polar axis

Step 3. Replace θ by π-θ

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

Step 4. Replace r by -r

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

Graph may or may not be symmetric with respect to pole

Step 5. Making the graph we get,