Answer
$r = 4~cos~2\theta$
This graph is a rose.
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Work Step by Step
$r = 4~cos~2\theta$
When $\theta = 0^{\circ}$, then $r = 4~cos~0^{\circ} = 4$
When $\theta = 15^{\circ}$, then $r = 4~cos~30^{\circ} = 3.46$
When $\theta = 30^{\circ}$, then $r = 4~cos~60^{\circ} = 2$
When $\theta = 45^{\circ}$, then $r = 4~cos~90^{\circ} = 0$
When $\theta = 60^{\circ}$, then $r = 4~cos~120^{\circ} = -2$
When $\theta = 75^{\circ}$, then $r = 4~cos~150^{\circ} = -3.46$
When $\theta = 90^{\circ}$, then $r = 4~cos~180^{\circ} = -4$
When $\theta = 120^{\circ}$, then $r = 4~cos~240^{\circ} = -2$
When $\theta = 135^{\circ}$, then $r = 4~cos~270^{\circ} = 0$
When $\theta = 150^{\circ}$, then $r = 4~cos~300^{\circ} = 2$
When $\theta = 180^{\circ}$, then $r = 4~cos~360^{\circ} = 4$
When $\theta = 210^{\circ}$, then $r = 4~cos~420^{\circ} = 2$
When $\theta = 240^{\circ}$, then $r = 4~cos~480^{\circ} = -2$
When $\theta = 270^{\circ}$, then $r = 4~cos~540^{\circ} = -4$
When $\theta = 300^{\circ}$, then $r = 4~cos~600^{\circ} = -2$
When $\theta = 330^{\circ}$, then $r = 4~cos~660^{\circ} = 2$
This graph is a rose.
We can see this graph below:
