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If z= sin omega find an expression for omega as a function of z that can be used to

  1. Jul 25, 2011 #1
    1. The problem statement, all variables and given/known data

    if z= sin (omega) find an expression for omega as a function of z that can be used to evaluate all possible values of sin^(-1) (3). Plot these values on the complex plane

    3. The attempt at a solution

    z= sin (omega)
    3= sin (omega)

    I don't know how to proceed from here. Please help
     
  2. jcsd
  3. Jul 25, 2011 #2

    Ray Vickson

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    Re: if z= sin omega find an expression for omega as a function of z that can be used

    For any w (real or complex) we have sin(w) = (1/2)*[exp(i*w) - exp(-i*w)], where i = sqrt(-1).

    RGV
     
  4. Jul 25, 2011 #3
    Re: if z= sin omega find an expression for omega as a function of z that can be used

    Actually, I believe the identity is [itex]\sin x = \frac{-i(e^{ix} - e^{-ix})}{2}[/itex].
     
  5. Jul 26, 2011 #4

    HallsofIvy

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    Re: if z= sin omega find an expression for omega as a function of z that can be used

    Or, equivalentlty,
    [tex]\frac{e^{ix}- e^{-ix}}{2i}[tex]
     
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