Answer
The two points of intersection are: $(2, \frac{\pi}{6})$ and $(2, \frac{5\pi}{6})$
Work Step by Step
$r = 4~sin~\theta$
$r = 1+2~sin~\theta$
To find the points of intersection, we can equate the expressions for $r$:
$4~sin~\theta = 1+2~sin~\theta$
$2~sin~\theta = 1$
$sin~\theta = \frac{1}{2}$
$\theta = \frac{\pi}{6}, \frac{5\pi}{6}$
We can find $r$:
$r = 4~sin~\theta$
$r = (4)~(\frac{1}{2})$
$r = 2$
The two points of intersection are: $(2, \frac{\pi}{6})$ and $(2, \frac{5\pi}{6})$
