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Homework Help: Calculus please help me solve this simple problem (I forgot how to): arcsin(4/5) = ?

  1. Jul 20, 2010 #1
    1. The problem statement, all variables and given/known data

    how do I solve this

    arcsin(4/5)

    note that I am not looking for about 53 degrees

    I believe I'm suppose to solve euler's formula for x

    i.e.
    sin (x) = (e^(ix) - e^(-ix))/(2i)
    where x is in radians
    hence I would do something like this

    sin (x) = (e^(ix) - e^(-ix))/(2i) = 4/5

    (e^(ix) - e^(-ix))/(2i) = 4/5
    solve the equation above for x

    this is were I need help if somebody could just show me quickly how to do this that would be great!!!

    If I remeber correctly I need to use cis(x) or something right?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 20, 2010 #2
    Re: Calculus please help me solve this simple problem (I forgot how to): arcsin(4/5)

    ok now this is an algebra 2 problem... I have goten far down to hear

    e^(ix) = (4i +/- 3)/5

    now how do I solve for x I feel really stupid now as this is algebra 2...

    can't use natural log right or the common log as

    ln( e^(ix) )
    does not equal ix

    so what do I do?
     
  4. Jul 20, 2010 #3
    Re: Calculus please help me solve this simple problem (I forgot how to): arcsin(4/5)

    Wait apparently I'm suppose to do something involving

    log(z) = ln|z| + i arg(z) for complex numbers z

    or something correct?
     
  5. Jul 21, 2010 #4

    hunt_mat

    User Avatar
    Homework Helper

    Re: Calculus please help me solve this simple problem (I forgot how to): arcsin(4/5)

    Try it and see.
     
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