anonymous
  • anonymous
how to parameterize x^3 + y^3 = 1?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Can you solve for y in terms of x?
anonymous
  • anonymous
z=0 by the way
amistre64
  • amistre64
x = cos^3(t) y= sin^3(t) z = 0 right?

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More answers

anonymous
  • anonymous
the answer is given as the same as what you put, but the powers are (2/3), not 3 and i'm unsure how they got that
amistre64
  • amistre64
I was close then :) I dont know how they got ^(2/3) either... id have to go back many years to remember ;)
amistre64
  • amistre64
its a cubic equation that crosses the x and y axis 3 times.... i see that much
anonymous
  • anonymous
i tried to use http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx to help but :( cant seem to figure it out
amistre64
  • amistre64
lets see if I can raeson this..... or muddy the waters :) x = rcos ; y = rsin ; 1 = sin^2 + cos^2 right?
amistre64
  • amistre64
r^3 (cos^3 + sin^3) = sin^2 + cos^2
anonymous
  • anonymous
yeah
amistre64
  • amistre64
I see where the ^1/3 is coming from.... just how to get it :)
anonymous
  • anonymous
it seems as though thats not too far away
anonymous
  • anonymous
Do you see that if you plug in x = (cos theta)^{2/3) and y=(sin theta)^(2/3) you get the original equation? That's why the answer is correct, but doesn't give much insight into how you were supposed to guess it.
amistre64
  • amistre64
yeah, the solution being correct is the easy part ;)
amistre64
  • amistre64
1 is also the "radius" or vector measure from the origin.... we could try that route.
amistre64
  • amistre64
are there any trig identitied we could utilize for this?
anonymous
  • anonymous
ermm, not that i can think of
amistre64
  • amistre64
r^3 (cos^3 + sin^3) = r^2 ; r^2 = 1 so r^3 = 1 ?
anonymous
  • anonymous
ye, i think r^3 must have to be 1
amistre64
  • amistre64
cos^3 + sin^3 = cos^2 + sin^2
amistre64
  • amistre64
cos^3 - cos^2 = sin^3 - sin^3 ??
amistre64
  • amistre64
typoed it...but you can see that lol
anonymous
  • anonymous
ye, i see lol...what do you have to do to a square power to make it ^2/3? do you cube root it?
amistre64
  • amistre64
yes; ^2/3 means cbrt(^2)
anonymous
  • anonymous
it's because you want cosx^2+sinx^2=1. So if x=cost^(2/3) when you plug it in, the square will distrbute in to leave cos^2
anonymous
  • anonymous
ok, i think i get it, thanks so much for the help!

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