Question

convert into cartesian coordinates: r^2sin2theta=2

Answer 1

\[x=rcos(\theta), y=rsin(\theta)\]\[r^2(\sin2\theta)=2\]We know that \[\sin(2\theta) = 2\sin(\theta)\cos(\theta)\]We plug this in, we got....\[r^2(2\sin(\theta)\cos(\theta))=2 \rightarrow 2(rsin(\theta))(rcos(\theta))=2\]\[2yx=2 \rightarrow yx=1 \rightarrow y=\frac{ 1 }{ x }\]

Answer 2

Thank you! So, I'm guessing I would do the same for r^2cos2theta=2, but solve for x, since the x=rcos(θ)

Answer 3

yeah, you got it. good luck

Answer 4

thank you. I appreciate it

Answer 5

you're welcome