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Math Help - Inverse of a Multiple Variable Function

  1. #1
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    Inverse of a Multiple Variable Function

    Ok here's the problem:
    F: R^2 -> R^2
    (t is theta)
    F(r,t) = (r*cos(t), r*sin(t))

    What is F^-1(0,0)?
    I know the answer is {(0,0) | -inf < t < inf }

    but I'm not exactly sure how to get to that point.
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  2. #2
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    Quote Originally Posted by merzbow View Post
    Ok here's the problem:
    F: R^2 -> R^2
    (t is theta)
    F(r,t) = (r*cos(t), r*sin(t))

    What is F^-1(0,0)?
    I know the answer is {(0,0) | -inf < t < inf }

    but I'm not exactly sure how to get to that point.
    lets start with this

    F(r,\theta)=(r\cos(\theta),r\sin(\theta))

    consider F(r,\theta)=(0,0)

    so we would need to know when

    r\cos(\theta)=0 \mbox{ and } r\sin(\theta)=0

    since cosine and sine are never zero at the same value of theta r must be zero. If that is the case then the equation

    0\cos(\theta)=0 \mbox{ and } 0\sin(\theta)=0

    is true for all values of theta so the inverse immage of (0,0) is

    [{(r,\theta)|r=0, -\infty < \theta < \infty}]
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  3. #3
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    Ah, thanks man. I knew it was something easy, I just couldn't figure it out.
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