1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Prove arcsin x for its logarithm form

  1. Apr 1, 2015 #1
    1. The problem statement, all variables and given/known data
    Given sin x = (eix - e-ix) / 2i,
    I want to prove that

    arcsin x = -i ln(ix + √1 - x2)

    2. Relevant equations
    I know about the Euler's formula and complex number. But I have never learnt about complex logarithms.

    3. The attempt at a solution
    I try to use x = sin y. But it seems not working. How to show that relation?
  2. jcsd
  3. Apr 1, 2015 #2


    Staff: Mentor

    Why not try working it backward? Take the arcsin x and substitute it into the first equation for x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted