Points of intersection with polar equations

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)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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