1
$\begingroup$

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...

$\endgroup$
  • $\begingroup$ Please type out the problem. It will be easier to read and as it is it is not searchable. Thanks! $\endgroup$ – Matthew Conroy Dec 12 '13 at 21:30
1
$\begingroup$

You got the angles right. Since $\sin 2 \theta = \cos 2 \theta$, $\theta = \pi/8, 5 \pi/8.$

Then,

$$r^2 = 3 \cos (\pi/4) \to r = \sqrt{\frac{3 \sqrt{2}}{2}}.$$

From here, $x = r \cos \theta$ and $y = r \sin \theta.$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.