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!

De Moivre's Formula Question

  1. Sep 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Use de Moivre's formula to derive the following trigonometric identites:

    [tex](a) cos3\theta = cos^3\theta - 3cos\theta sin^2\theta[/tex]

    [tex](b) sin3\theta = 3cos^2\theta sin\theta - sin^3\theta[/tex]

    2. Relevant equations

    3. The attempt at a solution
    The only way I have even figured out to solve this is by just doing
    [tex](cos\theta + isin\theta)^3 = (cos^3\theta - 3cos\theta sin^2\theta) + i(3cos^2\theta sin\theta - sin^3\theta) = cos3\theta + isin3\theta[/tex]

    but I fear that this is not what the problem is asking me to do. I think on (a) I should be factoring out [tex]cos^3\theta - 3cos\theta sin^2\theta = cos\theta(cos^2\theta - 3sin^2\theta)[/tex]

    should I then use the trig. formula that [tex]cos^2 - sin^2 = cos2\theta[/tex] but the 3 in front of sin is throwing me off. Anyone have a clue as how this problem is supposed to be done in the way the question is asking? Thank you
  2. jcsd
  3. Sep 3, 2009 #2


    User Avatar
    Homework Helper

    [tex](cos\theta + i sin \theta)^3 = cos 3 \theta+ i sin 3 \theta[/tex]

    Expand out the left side and notice that cos3θ is the real part.
  4. Sep 3, 2009 #3
    Yea rock that's what I did I just do not know if that's what the question is asking for because I do not think it is but I was wondering if anyone else had any ideas on what to do besides what you mentioned.
  5. Sep 3, 2009 #4


    User Avatar

    All the terms with i would = sin3θ, while all the terms without i (reals) would = cos3θ
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook