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Homework Help: Image of upper half-plane under the inverse sine

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data

    The problem is simply to find the image of the upper half-plane under the inverse sine function.

    2. Relevant equations

    The textbook defines the inverse sine in the following way. First, it defines arccos(w) = -i * log(w +/- sqrt(w^2 - 1)) and then it defines arcsin(w) = pi/2 - arccos(w).

    The problem doesn't specify what branches of the logarithm and square root should be used. I'm going to assume the principal branches.

    3. The attempt at a solution

    I've attempted to just break the inverse sine into a sequence of compositions and to, so to speak, push the upper half-plane through this sequence, but I've not been able to identify a breakdown into suitably elementary functions allowing me to determine the images.

    As for doing it directly, I'm just now seeing how to begin.
  2. jcsd
  3. Mar 17, 2010 #2
    I really hate to bump this, but does anybody have any ideas on how to approach the problem? I would significantly appreciate any advice!
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