Find all points of intersection of the curves $r^2=3\sin(2\theta)$ and $r^2=3\cos(2\theta)$

Find all points of intersection of the curves $r^2=3\sin(2\theta)$ and $r^2=3\cos(2\theta)$. Give your answers as ordered pairs in cartesian coordinates, in order of increasing radius and increasing angle.

So I set the two equations equal to one another, found that they intersect when theta equals $\dfrac\pi8$ and $\dfrac{5\pi}8$, plugged in $\dfrac\pi8$ to the square root of one of the equations to find $r$, and got the question wrong. Not sure why...

• Please type out the problem. It will be easier to read and as it is it is not searchable. Thanks! – Matthew Conroy Dec 12 '13 at 21:30

You got the angles right. Since $\sin 2 \theta = \cos 2 \theta$, $\theta = \pi/8, 5 \pi/8.$
$$r^2 = 3 \cos (\pi/4) \to r = \sqrt{\frac{3 \sqrt{2}}{2}}.$$
From here, $x = r \cos \theta$ and $y = r \sin \theta.$