Intersection pts of polar equations

[n00neimp0rtnt]

Homework Statement

I have to find the area of the region that lies inside the curves:

r = sin(θ)
r = sin(2θ)

The Attempt at a Solution

I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each other:

sin(θ) = sin(2θ)


arcsin both sides:
θ = 2θ

And I'm stuck. Analysis of the graph shows that the most crucial intersection point occurs at or very close to 75º, but I would like to be able to show that.

 

[Dick]

Taking arcsin of both sides will only give you some solutions. Try using sin(2x)=2*sin(x)*cos(x).

 

[n00neimp0rtnt]

Thanks a lot! In that case...

sin(θ) = 2sin(θ)cos(θ)
1 = 2cos(θ)
cos(θ) = 1/2
θ = π/3

That should help me get the rest of the problem, thanks again! =]