How do you convert #r^2=sin2(theta)# to rectangular form?

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Answer 1 · 2016-02-08T01:18:27

Use the following identities:

#sin2theta=2costhetasintheta#
#x=rcostheta#
#y=rsintheta#
#x^2+y^2=r^2#

Using the above identities ...

#r^2=sin2(theta)#

#x^2+y^2=2(x/r)(y/r)=(2xy)/r^2=(2xy)/(x^2+y^2)#

Now simplify ...

#(x^2+y^2)^2=2xy#

#x^4+2x^2y^2+y^4-2xy=0#

hope that helped

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