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    grr i was doing maths revision and decided to pick the MOST EVIL QUESTION in the whole wide world!

    x = ?sin? + cos?
    y = ?cos? - sin?

    find the equation of the curve...

    i do know that sin²? + cos²? = 1 plays a part, but im confused as what to do
    can anyone help? (i need a dummy's guide to answering this question :rolleyes: )
    any help is greatly appreciated
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    grr
    the qn mark = theta
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    (Original post by hel437)
    grr i was doing maths revision and decided to pick the MOST EVIL QUESTION in the whole wide world!

    x = ?sin? + cos?
    y = ?cos? - sin?

    find the equation of the curve...

    i do know that sin²? + cos²? = 1 plays a part, but im confused as what to do
    can anyone help? (i need a dummy's guide to answering this question :rolleyes: )
    any help is greatly appreciated
    I am sure I remember doing this one ages ago...

    x + y = 2cosθ
    x - y = 2sinθ

    => (x + y)² + (x - y)² = 2²cos²θ + 2²sin²θ = 2²

    => x² + 2xy + y² + x² - 2xy + y² = 4

    => 2x² + 2y² = 4

    => x² + y² = 2

    Is that right?
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    i might just be having a stupid day...but i dont get how you get x+ y = 2cos theta..or the x - y = 2sin theta
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    (Original post by hel437)
    i might just be having a stupid day...but i dont get how you get x+ y = 2cos theta..or the x - y = 2sin theta
    x = sinθ + cosθ
    y = cosθ - sinθ

    so: x + y = sinθ + cosθ + cosθ - sinθ = 2cosθ

    and: x - y = sinθ + cosθ - cosθ + sinθ = 2sinθ
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    but its theta sin theta in x and theta cos theta in y...argh! so confused..
    im really appreciating your help
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    (Original post by hel437)
    but its theta sin theta in x and theta cos theta in y...argh! so confused..
    im really appreciating your help
    Oh is it! Sorry...

    Are you sure?

    Where is this from?
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    its ex 4b question 1 vi) in the P3 MEI text book. i dont think i copied it down wrong, bt i dont have access to the textbook at this very moment. it wasnt an exam question, so its not hugely important. but its starting to annoy me now.
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    Do you have an answer?
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    x = φsinφ + cosφ
    y = φcosφ - sinφ

    x² = φ²sin²φ + 2φsinφcosφ + cos²φ
    y² = φ²cos²φ - 2φcosφsinφ + sin²φ

    x² + y² = φ²(sin²φ + cos²φ) + (cos²φ + sin²)
    x² + y² = φ² + 1
    r² = φ² + 1
    r = √(φ² + 1)
    ==========

    Which is the polar eqn of a spiral.
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    i *just* realised i read the stupid question wrong. all i had to do was find dy/dx *bangs head on wall*
    apologies to all those of you who tried (and succeeded in some cases) to work it out!
    i really am having a stupid day
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    this question just asks for the differential so its just
    dy/dx = dy/d0 x d0/dx

    d0/dx= 1/dx/d0

    dy/dx= (-θsinθ+cosθ- cosθ )/(θcosθ+sinθ- sinθ )
    dy/dx= -θsinθ/θcosθ
    dy/dx= -tanθ
 
 
 
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