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What is sin-1(2i) equal?

  1. May 2, 2009 #1
    I could not found any answer to this question: What is sin-1(2i) equal?
     
  2. jcsd
  3. May 2, 2009 #2

    matt grime

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    Re: Multi-Valuedness

    sin(x) = (exp(ix)-exp(-ix))/2i

    Firstly let y=exp(ix) and subs in

    ( y + 1/y)/2i=2i

    solve for y, then for x.
     
  4. May 2, 2009 #3

    HallsofIvy

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    Re: Multi-Valuedness

    Since you titled this thread "Multi-Valuedness", note that solving (y+ 1/y)/2i= 2i will involve solving a quadratic function so you may have two values for y. Then solving y= exp(ix) with both values of involves taking the logarithm which adds multiples of [itex]2\pi i[/itex].
     
  5. May 2, 2009 #4
    Re: Multi-Valuedness

    For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?
     
  6. May 2, 2009 #5

    matt grime

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    Re: Multi-Valuedness

    Yes - I can't even seem to follow my own suggestion.
     
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