Points of intersection with polar equations

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The discussion focuses on finding the points of intersection between the polar curves r² = sin(2θ) and r² = cos(2θ). The user initially sets the equations equal to each other, leading to the equation sin(2θ) = cos(2θ). They derive a more complex expression but express confusion about the next steps. A suggestion is made to simplify the problem by dividing by cos²(θ) to solve for tan(2θ) = 1. The user acknowledges the oversight and humorously admits to a temporary lapse in factoring skills.
n00neimp0rtnt
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Homework Statement


I have to find all of the points of intersection of the curves...

r2 = sin(2θ)
r2 = cos(2θ)


The Attempt at a Solution



sin(2θ) = cos(2θ)
2sinθcosθ = cos2θ - sin2θ
2sinθcosθ - cos2θ = -sin2θ
cosθ(2sinθ - cosθ) = -sin2θ

This is where I'm having a problem, I'm not sure what to do from here.
 
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Why not just divide by cos2θ and solve tan2θ=1?
 
Aww. Yep you're right, thanks. (Today is not a math day for me; I temporarily forgot how to factor earlier, haha)
 

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