Question

Write the following polar equation in Cartesian coordinates:

r = sin (2θ) becomes
_______ = 0

(Write the equation so any square root has a positive coefficient.)

Thank you!

Answer 1

Note that \(\large r=\sin(2\theta) = 2\sin\theta\cos\theta\). Then multiply both sides by \(\large r^2\) to get \[\large r^3= 2r^2\sin \theta\cos\theta \implies r^3 = 2 (r\sin\theta)(r\cos\theta) \implies \ldots\] Can you take things from here? :-)

Answer 2

Yes! thank you @ChristopherToni I wasn't sure how to distribute the r^2 as you did. My algebra is shaky. THanks so much!