Is sin-1(2i) Equal to 0.5 + 1.31696i?

symsane · May 2, 2009

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

matt grime · May 2, 2009

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 · May 2, 2009

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 [itex]2\pi i[/itex].

Big-T · May 2, 2009

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

matt grime · May 2, 2009

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

Is sin-1(2i) Equal to 0.5 + 1.31696i?

Discussion

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