Results 1 to 3 of 3

Math Help - calculating cos(nθ) and sin(nθ) with de Moivre

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    15

    calculating cos(nθ) and sin(nθ) with de Moivre

    I'm not sure in which subforum I should post this, feel free to move it to another subforum.

    From my course:

    (cos(\theta) + jsin(\theta))^3 = cos(3\theta) + jsin(3\theta)
    cos^3(\theta) + 3jcos^2(\theta)sin(\theta) - 3cos(\theta)sin^2(\theta) - jsin^3(\theta) = cos(3\theta) + jsin(3\theta)
    <->
    cos(3\theta) = cos^3(\theta) - 3cos(\theta)sin^2(\theta) and sin(3\theta) = 3cos^2(\theta)sin(\theta) - sin^3(\theta)

    I have no problem with the first two lines, I don't understand how you can logically deduce the last line from the first two lines.
    After all, cos(3\theta) = cos^3(\theta) + 3jcos^2(\theta)sin(\theta) - 3cos(\theta)sin^2(\theta) - jsin^3(\theta) - jsin(3\theta)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    In order to get the third line, they equated the real parts of both sides of the second line, and the imaginary parts of both sides of the second line.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    15
    So that is comparable to when you would seperate X and Y in an ´ordinary` equation?
    File:Complex conjugate picture.svg - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. De Moivre's Theorem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 18th 2010, 01:43 PM
  2. [SOLVED] De Moivre's Theorem
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: November 18th 2010, 02:06 PM
  3. De Moivre's Theorem
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: August 31st 2009, 06:45 AM
  4. A little help with de Moivre's
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 15th 2009, 12:24 PM
  5. de moivre's thm
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 20th 2008, 01:22 AM

Search Tags


/mathhelpforum @mathhelpforum