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C4 parametric equations help

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    A curve has parametric equations: x = 2cos2t y = 6sint

    a) find the gradient of the curve at the point where t = pi/3 (done this)

    b) find a cartesian equation of the curve in the form:
    y = f(x), -k < x < k


    No idea what to do for b =S
  2. Offline

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    Is there any way you can eliminate t from the equations, maybe using a trigonometric identity?
  3. Offline

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    Tried using cos2t as 1 - 2sin^2t, but it didn't seem to work out.
  4. Offline

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    As far as I'm aware that should work out...

    What did you get for 2sin^2(t) then?
  5. Offline

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    Erm... y = 6 - root(18x)
    Can't find a mark scheme to check, but no idea where the K comes into it x_X
  6. Offline

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    it should be y=3root(2-x)
    x=2(1-2sin^2t) y=6sint
    y^2=36sin^2t
    (y^2)/36=sin^2t

    x=2-4sin^2t
    sub y
    x=2-((Y^2)/9)

    multiply through by 9

    9x=18-(Y^2)
    Y=root(18-9x)

    thats what i get atleast

    so -2<x<2
  7. Offline

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    (Original post by nitinkf)
    it should be y=3root(2-x)
    x=2(1-2sin^2t) y=6sint
    y^2=36sin^2t
    (y^2)/36=sin^2t

    x=2-4sin^2t
    sub y
    x=2-((Y^2)/9)

    multiply through by 9

    9x=18-(Y^2)
    Y=root(18-9x)

    thats what i get atleast

    so -2<x<2
    I concur.
  8. Offline

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    Put x=2cos2t into the form x=2(2(cost)^2-1) or x=4(cost)^2-2

    then y=6sint into Y^2=36(sint)^2

    Then into identity (Sint)^2 + (cost)^2 = 1 in order to eliminate paramiter

    The constant bit (K) is to show that you undersatnd the maximum and minimum x values of the cartesian equation.
  9. Offline

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    Got it now, thanks all
  10. Offline

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    For this one I got


    EDIT: Just realised I forgot the 6! Dammit...
  11. Offline

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    I've got the same question but can anyone help me with part a? I used the chain rule on it and and the whole dx/dt=1/(dt/dx) but I want to check my answer? :3
  12. Offline

    (Original post by revilowaldow)
    I've got the same question but can anyone help me with part a? I used the chain rule on it and and the whole dx/dt=1/(dt/dx) but I want to check my answer? :3

    I make it -\dfrac{\sqrt{3}}{2}

    If you get anything else and want someone to check it, then post your working.

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Updated: July 19, 2012
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