(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Convert the polar equation to rectangular form.

r=2sin(3θ)

2. Relevant equations

3. The attempt at a solution

I can expand this out to

[tex]r=2(\sin\theta\cos2\theta+\cos\theta\sin2\theta)[/tex]

multiply both sides by r

[tex]r^2=2r(\sin\theta\cos2\theta+2r\cos\theta\sin2\theta)[/tex]

simplify

[tex]r^2=2y\cos2\theta+2x\sin2\theta)[/tex]

Then I could expand the 2θ and get

[tex]r^2=2y\cos^2\theta-2y\sin^2\theta+4x\sin\theta\cos\theta[/tex]

I'm not sure where to go from here.

Plugging it into [tex]x^2+y^2=r^2[/tex] from here dosen't seam to help.

The answer is supposed to be: [tex](x^2+y^2)^2=6x^2y-2y^3[/tex]

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# Homework Help: Converting A Polar Equation to Rectangular Form

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