- #1
themadhatter1
- 140
- 0
Homework Statement
Convert the polar equation to rectangular form.
r=2sin(3θ)
Homework Equations
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]