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Size:  380.3 KB hi I don't quite get how the answer is obtained in part a. Attachment 616026616028here is my working but the actual answer is all squared but mine isn't.

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    if you leave it square you don't have to do the plus or minus thing with the square root.
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    (Original post by coconut64)
    hi I don't quite get how the answer is obtained in part a. here is my working but the actual answer is all squared but mine isn't.

    Thanks
    As said above, you can't say that \sin(\theta)=\sqrt{1-x^2} as then \sin(\theta)\geq 0 whereas we can also have \sin(\theta)<0 as we are not given any restrictions on \theta. To avoid any \pm notation and whatnot, it is easier to leave it as everything squared.

    EDIT:
    Just attaching the graphs of the 3 equations. The green curve is parametric, the red dots is your Cartesian equation, and the black dots is the correct Cartesian equation.


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    (Original post by RDKGames)
    As said above, you can't say that \sin(\theta)=\sqrt{1-x^2} as then \sin(\theta)\geq 0 whereas we can also have \sin(\theta)<0 as we are not given any restrictions on \theta. To avoid any \pm notation and whatnot, it is easier to leave it as everything squared.

    EDIT:
    Just attaching the graphs of the 3 equations. The green curve is parametric, the red dots is your Cartesian equation, and the black dots is the correct Cartesian equation.


    Thanks for the detailed explanation. I have only started on this topic, what does it actually mean by parametric equation? So in the last graph, it shows that the graph can be negative as well so surely if it's square rooted then it still makes sense as the graph can also be negative ...

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    (Original post by coconut64)
    Thanks for the detailed explanation. I have only started on this topic, what does it actually mean by parametric equation? So in the last graph, it shows that the graph can be negative as well so surely if it's square rooted then it still makes sense as the graph can also be negative ...

    Thanks
    Parametric equations are a set of equations is that express different quantities (x and y in your case) in terms of a different variables, t in your case, which are considered as a parameters. You will only encounter single variable parameterisation in C4. The more you do of this chapter the more this will make sense later.

    To answer that question is a bit awkward considering this question, so I'll pick a single counter-example to show you why your equation doesn't quite work out. Let t=-\frac{\pi}{4}. Then x=\frac{\sqrt{2}}{2} and y=-1. Your found equation would give y=2(\frac{\sqrt{2}}{2})\sqrt{1-(\frac{\sqrt{2}}{2})^2}=1 \not= -1 so your equation fails for a perfectly defined point. However it WOULD work out if you were to square both sides.

    Keep in mind though that your answer would be considered correct if you took \sin(\theta) = \pm \sqrt{1-x^2} instead.
 
 
 
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