Chapter 9.6, Problem 30E

To determine

To calculate: To graph the polar equation

Explanation of Solution

Given information: Polar equation is $r=3+6\cos \theta$

Calculation:

Polar equation is given as follows:

  $r=3+6\cos \theta$

Above equation is type of Limacons with inner loop

Plotting the below points

  $\left(0,\frac{2\pi }{3}\right),\left(9,0\right),\left(3,\frac{\pi }{2}\right),\left(3,\frac{3\pi }{2}\right),\left(-3,\pi \right)$

Also, polar equation is symmetric with respect to polar axis and passes through the pole

Graph of polar equation is as follows:

  

Conclusion:

Hence, graph is sketched