How do you convert $r= 5(sin(2x))$ into cartesian form?

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Answer 1 · 2016-04-15T17:16:03

$x^6+2x^4y^2+x^2y^4+y^2x^4+2x^2y^4+y^6-100x^2y^2=0$

Use Formula $sin2A=2sinAcosA$

$r=5(2sinxcosx)$

$r=10sinxcosx$

$rxxr^2=10xxrsinx xx rcosx$

$sqrt(x^2+y^2) (x^2+y^2)=10 xy$

$[sqrt(x^2+y^2) (x^2+y^2)]^2=(10 xy)^2$

$(x^2+y^2)(x^2+y^2)^2=100x^2y^2$

$(x^2+y^2)(x^4+2x^2y^2+y^4)=100x^2y^2$

$x^6+2x^4y^2+x^2y^4+y^2x^4+2x^2y^4+y^6-100x^2y^2=0$

How do you convert r= 5(sin(2x))r= 5(sin(2x)) into cartesian form?