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Parametric Equations and cartesian equation

  • #1
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(1)If you are given the parametric equations [itex] x = sin(2\pi\t) [/itex] [itex] y = cos(2\pi\t) [/itex] and [itex] 0\leq t\leq 1 [/itex] how would you find the cartesian equation for a curve that contains the parametrized curve?

Using the identity [itex] \sin^{2}\theta + cos^{2}\theta = 1 [/itex] would it be [itex] x^{2} + y^{2} = 1 [/itex]?

Thanks
 

Answers and Replies

  • #2
EnumaElish
Science Advisor
Homework Helper
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Sorry... What does anything have to do with t? Isn't t part of the problem? If so, should it not be part of the solution as well?
 
  • #3
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Are you sure x and y are independent of t?? If so, the cartsian equation is just the point (0,1)
 
  • #4
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come on its a typo.... [itex] x = \sin(2\pi t ), y = \cos(2\pi t ) [/itex]

thanks
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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plugpoint, you were the one who made the typo- "Sorry, it was a typo" would be better than "Come on its a typo"!

Yes, you are correct, since [itex]sin^2(2\pi t)+ cos^2(2\pi t)[/itex].
You should also note that, as t goes from 0 to 1, [itex]2\pi t[/itex] goes from 0 to [itex]2\pi[/itex] so this would be exactly once around the circle.
 
  • #6
1,235
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sorry about that. I was actually saying that to myself, because I was annoyed that I always make typos with Latex. Sorry To Tsar and EnumaFish. And thank you HallsofIvy for helping me

:smile:
 

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