Answer
$r = 1 - cos~\theta$
$\theta$ in $[0,2\pi)$
This graph is a cardioid.
We can see the graph below:
Work Step by Step
$r = 1 - cos~\theta$
$\theta$ in $[0,2\pi)$
When $\theta = 0$:
$r = 1 - cos 0= 0$
When $\theta = \frac{\pi}{4}$:
$r = 1- cos~\frac{\pi}{4} = 1 - \frac{\sqrt{2}}{2} = 0.29$
When $\theta = \frac{\pi}{2}$:
$r = 1 - cos~\frac{\pi}{2} = 1$
When $\theta = \frac{3\pi}{4}$:
$r = 1 - cos~\frac{3\pi}{4} = 1 + \frac{\sqrt{2}}{2} = 1.71$
When $\theta = \pi$:
$r = 1 - cos~\pi = 2$
When $\theta = \frac{5\pi}{4}$:
$r = 1 - cos~\frac{5\pi}{4} = 1+\frac{\sqrt{2}}{2} = 1.71$
When $\theta = \frac{3\pi}{2}$:
$r = 1 - cos~\frac{3\pi}{2} = 1$
When $\theta = \frac{7\pi}{4}$:
$r = 1 - cos~\frac{7\pi}{4} = 1 - \frac{\sqrt{2}}{2} = 0.29$
This graph is a cardioid.
We can see the graph below:
