anonymous
  • anonymous
Find the rectangular equation of the parametric equations x=cost an y=sin^2t+1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
i guess you can use the fact that \(\sin^2(x)=1-\cos^2(x)\)
anonymous
  • anonymous
or rather \[\sin^2(t)=1-\cos^2(t)\]
anonymous
  • anonymous
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

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anonymous
  • anonymous
i am not exactly sure what "rectangular" means but since \(x=\cos(t)\) then you have \[y=1-x^2+1=x^2\]
anonymous
  • anonymous
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
  • anonymous
ok i screwed up , it is \(y=-x^2\)
anonymous
  • anonymous
what is the answer?
anonymous
  • anonymous
y=2-x^2
anonymous
  • anonymous
\[\begin{cases}x=\cos t\\y=\sin^2t+1\end{cases}\] As @satellite73 said, \[y=(1-\cos^2t)+1=2-\cos^2t\] And \[x^2=\cos^2t\] So, \(y=2-x^2\).
anonymous
  • anonymous
i am still not understanding how you are going from here x=cost y=sin2t+1 to y=(1−cos2t)+1=2−cos2t
anonymous
  • anonymous
It's the identity satellite mentioned: \[\sin^2t+\cos^2t=1~\Rightarrow~\sin^2t=1-\cos^2t\]
anonymous
  • anonymous
oh alright, thanks so much!

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