# What is sin-1(2i) equal?

1. May 2, 2009

2. May 2, 2009

### matt grime

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.

3. May 2, 2009

### HallsofIvy

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 $2\pi i$.

4. May 2, 2009

### Big-T

Re: Multi-Valuedness

For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?

5. May 2, 2009

### matt grime

Re: Multi-Valuedness

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