Answer:
[tex]\theta=0(\:pole),\frac{\pi}{3},\frac{5\pi}{3}[/tex]
Step-by-step explanation:
The given system of polar equations are:
[tex]r=\sin \theta[/tex]
[tex]r=\sin 2\theta[/tex]
We equate both equations to get:
[tex]\sin 2\theta=\sin \theta[/tex]
We rewrite to get:
[tex]\sin 2\theta-\sin \theta=0[/tex]
Apply the double angle property to get:
[tex]2\sin \theta \cos \theta-\sin \theta=0[/tex]
Factor now to get:
[tex]\sin \theta( 2\cos \theta-1)=0[/tex]
[tex]\implies \sin \theta=0\:or\:\cos \theta=0.5[/tex]
Hence [tex]\theta=0,\frac{\pi}{3},\frac{5\pi}{3}[/tex]
