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I could not found any answer to this question: What is sin

^{-1}(2i) equal?You are using an out of date browser. It may not display this or other websites correctly.

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- Thread starter symsane
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- #1

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

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- #2

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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

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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].

- #4

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

- #5

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

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