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Thread: Parametric Equations

  1. #1
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    Parametric Equations

    I need to find the point were the curve crosses itself:

    $\displaystyle x=2-\pi \cos(t)$
    $\displaystyle y=2t-\pi \sin(t)$

    This is really tricky; I can't think of any method to use to solve this (other than plotting points).
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  2. #2
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    Quote Originally Posted by adkinsjr View Post
    I need to find the point were the curve crosses itself:

    $\displaystyle x=2-\pi \cos(t)$
    $\displaystyle y=2t-\pi \sin(t)$

    This is really tricky; I can't think of any method to use to solve this (other than plotting points).
    You need to find the parameter values s, t, that satisfy

    $\displaystyle 2-\pi \cos t=2-\pi \cos s$ and $\displaystyle 2t-\pi\sin t=2s-\pi \sin s$

    from the first equation you get that $\displaystyle \cos t=\cos s$, hence $\displaystyle s=\pm t+n\cdot 2\pi$.

    Now plug that value of s into the second equation and hope for the best...
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