Answer
$r = 8+6~cos~\theta$
This graph is a cardiod.
We can see this graph below:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ceb60360-be07-48b2-9b56-0b0859286e49/result_image/1530952843.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011116Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=f81f8d2e2c8a3c891267b2f972301b78093d611d500fa81677e59f11eb7eb84e)
Work Step by Step
$r = 8+6~cos~\theta$
When $\theta = 0^{\circ}$, then $r = 8+6~cos~0 = 14$
When $\theta = 60^{\circ}$, then $r = 8+6~cos~60^{\circ} = 11$
When $\theta = 90^{\circ}$, then $r = 8+6~cos~90^{\circ} = 8$
When $\theta = 120^{\circ}$, then $r = 8+6~cos~120^{\circ} = 5$
When $\theta = 180^{\circ}$, then $r = 8+6~cos~180^{\circ} = 2$
When $\theta = 240^{\circ}$, then $r = 8+6~cos~240^{\circ} = 5$
When $\theta = 270^{\circ}$, then $r = 8+6~cos~270^{\circ} = 8$
When $\theta = 300^{\circ}$, then $r = 8+6~cos~300^{\circ} = 11$
This graph is a cardiod.
We can see this graph below:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ceb60360-be07-48b2-9b56-0b0859286e49/steps_image/small_1530952843.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011116Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=362baa49d6949f18449af8d3f592a0a10592cdbb57b781f3945ba8881859b551)