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

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Answer 1 · 2016-04-15T17:16:03

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

Use Formula $sin 2 A = 2 sin A cos A$ $sin2A=2sinAcosA$

$r = 5 (2 sin x cos x)$ $r=5(2sinxcosx)$

$r = 10 sin x cos x$ $r=10sinxcosx$

$r \times r^{2} = 10 \times r sin x \times r cos x$ $rxxr^2=10xxrsinx xx rcosx$

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

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

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

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

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

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