anonymous
  • anonymous
Convert r=1-Cos[2x] into rectangular. I tried using the trig identity of Cos2x which was 1-2(Cosx)^2, and multiplying r^2 on both sides, but I didn't get anywhere. Help, please?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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amistre64
  • amistre64
r = 1- cos(2x) correct?
amistre64
  • amistre64
r^2 = r - r cos(2x) right?
amistre64
  • amistre64
cos(2x) = cos^2 - sin^2

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amistre64
  • amistre64
maybe better like this: r = 1 - (cos^2(x) - sin^2(x)) r = 1 - cos^2(x) + sin^2(x) r = 1 -cos^2 + (1 - cos^2) r = 2 - 2 cos^2 r/2 = = 1- cos^2 r/2 = sin^2
amistre64
  • amistre64
any luck with this? :)
mathmagician
  • mathmagician
correct answer is \[(x^2+y^2)^3=4y^4\] rewrite the equation \[r=1-\cos(2t)\] to \[r=2\sin^2(t)\] and use identities: \[r^2=x^2+y^2 and \sin(t)=y/r\]

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