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

1. Jul 25, 2011

### blueyellow

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)

2. Jul 25, 2011

### Ray Vickson

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

3. Jul 25, 2011

### Strants

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 $\sin x = \frac{-i(e^{ix} - e^{-ix})}{2}$.

4. Jul 26, 2011

### HallsofIvy

Staff Emeritus
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]