Find the points of intersection of the graphs of the equations r = 1 + sin θ,       r = 3 sin θ

$\begin{array}{rcl}r & =& 1 + \sin \theta , \\ r & =& 3 \sin \theta \end{array}$

To find: The points of intersection of the graphs of the equations.

Equate both equations, 

$\begin{array}{rcl}1+\sin \theta & =& 3 \sin \theta \\ 3 \sin \theta - \sin \theta & =& 1\\ 2 \sin \theta & =& 1\\ \sin \theta & =& \frac{1}{2} ...\left(i\right)\end{array}$

Since the sine function is positive in the first and the second quadrant.

Thus, the solution will be $\theta =\frac{\pi }{6}+2\pi n,\hspace{0.17em}\theta =\frac{5\pi }{6}+2\pi n$, where n is any integer.