Results 1 to 2 of 2

Thread: Sine and Cosine of i (imaginary unit)

  1. #1
    Mar 2008

    Sine and Cosine of i (imaginary unit)

    The following is my working for the Sine and Cosine of the imaginary unit, i.

    Substituting x=i gives
    Squaring both sides
    Substituing 1-(sin(i))^2 for (cos(i))^2 gives
    Rearranging the original equation in terms of cos(i) gives
    Substituing this back into e^{-2}=(1-2((sin(i))^2)+2i(sin(i)cos(i)) gives
    e^{-2}=(1-2((sin(i))^2)+2i(sin(i))(e^{-1}) -2(i^2)((sin(i))^2)
    Rearranging for sin(i) gives
    sin(i)={{1 - e^2} \over 2ei}
    Then to find Cos(i): Substituting back into the original equation gives
    cos(i)={{1 + e^2} \over 2e}

    The problem is that all the sources I can find for the sine and cosine of i on the internet say
    sin(i) = {{e - 1/e} \over 2} \, i or {{e^2 - 1} \over 2e} \, i and
    cos(i)={{e + 1/e} \over 2} or {{e^2 + 1} \over 2e}.

    EDIT: I found my mistake in Cos(i), and now have the same as the internet for cos(i). BUT, I obtained my cos(i) from putting my sin(i) into the original equation and still got the right answer, which makes it even more puzzling.

    As you can see, my answers are very close to the others, I just can't figure out where the difference in signs comes from... also, is there any difference if the i is put outside the fraction like they have, or on the bottom like I work it to be?

    If I've made any typos or not made anything clear enough, just point it out and I'll change the original post.

    Thanks, Spud.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Oct 2007
    London / Cambridge
    Double posting is agains the rules. you already posted the question here and i answered it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. natural log and imaginary unit question
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Nov 27th 2009, 01:26 PM
  2. real number value for imaginary unit
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 28th 2009, 08:36 AM
  3. Imaginary unit
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: Mar 26th 2009, 03:44 PM
  4. cosine and sine..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 4th 2008, 01:49 AM
  5. Sine and Cosine of i (imaginary unit)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 2nd 2008, 08:01 AM

Search Tags

/mathhelpforum @mathhelpforum