Parametric Equations and cartesian equation

[courtrigrad]

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

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

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... $x = \sin(2\pi t ), y = \cos(2\pi t )$

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 $sin^2(2\pi t)+ cos^2(2\pi t)$.
You should also note that, as t goes from 0 to 1, $2\pi t$ goes from 0 to $2\pi$ 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