Question

Find all point of intersection of
r=sin2q and r=sinq

Answer 1

sin(2q) = sin(q)
from double angle identity
--> sin(2q) = 2sin(q)cos(q)

2sin(q)cos(q) = sin(q)
2sin(q)cos(q) - sin(q) = 0
sin(q) (2cos(q) -1) = 0

--> q = 0,pi/3,pi, 5pi/3, 2pi