What is sin-1(2i) equal?

[symsane]

I could not found any answer to this question: What is sin^-1(2i) equal?

 

[matt grime]

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.

 

[HallsofIvy]

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 $2\pi i$.

 

[Big-T]

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

 

[matt grime]

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