Parametric Equations and cartesian equation

[courtrigrad]

(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

 

[EnumaElish]

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?

 

[Tzar]

Are you sure x and y are independent of t?? If so, the cartsian equation is just the point (0,1)

 

[courtrigrad]

come on its a typo... [itex] x = \sin(2\pi t ), y = \cos(2\pi t ) [/itex]

thanks

 

[HallsofIvy]

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.

 

[courtrigrad]

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