Find the rectangular equation of the parametric equations x=cost an y=sin^2t+1

Question

anonymous · Answer

i guess you can use the fact that $\sin^2(x)=1-\cos^2(x)$

anonymous · Answer

or rather 
$$\sin^2(t)=1-\cos^2(t)$$

anonymous · Answer

i do not believe that this is correct because you need to turn it into a rectangular equation, that is probably the first step, but i need help convverting into rectangular @satellite73

anonymous · Answer

i am not exactly sure what "rectangular" means but since $x=\cos(t)$ then you have $$y=1-x^2+1=x^2$$

anonymous · Answer

maybe you refer to rectangular as cartesian? (i think thats the word) and i have the answer, I just am trying to understand the process

anonymous · Answer

ok i screwed up , it is $y=-x^2$

anonymous · Answer

what is the answer?

anonymous · Answer

y=2-x^2

anonymous · Answer

$$\begin{cases}x=\cos t\y=\sin^2t+1\end{cases}$$
As @satellite73 said,
$$y=(1-\cos^2t)+1=2-\cos^2t$$
And
$$x^2=\cos^2t$$
So, $y=2-x^2$.

anonymous · Answer

i am still not understanding how you are going from here x=cost   y=sin2t+1   to 

y=(1−cos2t)+1=2−cos2t

anonymous · Answer

It's the identity satellite mentioned:
$$\sin^2t+\cos^2t=1~\Rightarrow~\sin^2t=1-\cos^2t$$

anonymous · Answer

oh alright, thanks so much!