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Inverse of sinc

  1. Jan 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Does anyone know the inverse of [tex]sinc(x)[/tex] or [tex]\frac{sin(x)}{x}[/tex]?

    2. Relevant equations

    If [tex]sinc(x)=a[/tex], [tex]x=f(a)[/tex]. What is [tex]x[/tex] in function of [tex]a[/tex]?

    3. The attempt at a solution

    If I knew the exact value of [tex]a[/tex], I could find the corresponding value of [tex]x[/tex] graphically. But how do I find [tex]x[/tex] if I didn't know [tex]a[/tex]?
     
    Last edited: Jan 5, 2009
  2. jcsd
  3. Jan 5, 2009 #2

    HallsofIvy

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    "sin(x)" itself does not have a true inverse. If you restrict x to between 0 and [itex]\pi[/itex], sin(x) and sinc(x) have inverses but the inverse of sinc(x) cannot be written in terms of simple functions. If y= sinc(x)= sin(x)/x, then finding the inverse function would be the same as solving xy= sin(x) for x which cannot be done in terms of simple functions.
     
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