translate this polar equation into a rectangular form:

Question

rsin(2theta)=sin(theta)

My answer:

r2sin(theta)cos(theta)=sin(theta)
2rcos(theta)=1
2x=1
x=1/2

This is the only answer I can get and someone told me it's wrong. Would someone please help me with this

Answer 1

or maybe the answer is:

y=2xy

but that's kind of weird

Answer 2

I don't know if this is right, but this is how I would work it.

rsin (2 theta) = sin (theta)

r (2 sin(theta) 2cos(theta)) = sin (theta) divide both sides by 2 sin
r 2 cos (theta) = 1/2 divide both sides by 2
r cos (theta) = 1/4
x = 1/4