from parametric to x and y

[allegansveritatem]

Here are the instructions:


I am trying to find an equation in x and y to replace this parametric system:


Now, if only x=cos(t) instead of cos(2t) I would be in a good place. But as things stand this thing feels kinda mean and dreadful. Here is about as far as I get( I have gotten a little farther but such was the futility of the attempt that the following is as good a representative of my progress as any:


So...how to proceed?

 

[pka]

\(x=\cos(2t),~\;y=\sin(t):~\;~\;\pi\le t\le\pi\)
\(x=\cos(2t)=1-2\sin^2(t)=1-2y^2\).

 

[allegansveritatem]

\(x=\cos(2t),~\;y=\sin(t):~\;~\;\pi\le t\le\pi\)
\(x=\cos(2t)=1-2\sin^2(t)=1-2y^2\).

I have just copied your post and will work on it later in the day. It looks good but I have to work through it--I don't understand it as it is, but I will after I have studied it a little. Have to run right now. Thanks for the post.

 

[allegansveritatem]

\(x=\cos(2t),~\;y=\sin(t):~\;~\;\pi\le t\le\pi\)
\(x=\cos(2t)=1-2\sin^2(t)=1-2y^2\).

I went over your post again this afternoon, understood what you did (very neat trick) and went back and worked the problem out pretty much along the lines you did. Here is my result: