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!

Fourier series help

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi. I want to find the fourier series of

    sin^2 x + sin ^3x

    and sin θ = [e^iθ - e-iθ]/2i

    2. Relevant equations



    3. The attempt at a solution

    So if i use sin x = [e^ix - e-ix]/2i I will get for the first term:

    [e^2ix + e^-2ix -2]/-4

    I can do the same for the second term but what do i do from here..? I'm not sure how to integrate these.
     
  2. jcsd
  3. Feb 2, 2012 #2
    Your Fourier coefficients for sin2x are simply ±1/(2i) for exp(±2ix), similar for all the other terms
     
  4. Feb 2, 2012 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You don't need to integrate.

    Hint: Use ##\cos \theta = \frac{e^{i\theta}+e^{-i\theta}}{2}## to rewrite

    $$-\frac{e^{i(2x)} + e^{-i(2x)} - 2}{4} = \ ?$$
     
  5. Feb 2, 2012 #4
    isn't that just cos^2x ?? It should most likely be something else but that's the only way i see it being re written as cos. That just brings me back to the starting point so yeah..heh
     
  6. Feb 2, 2012 #5

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    No, you have to get the algebra right. :wink: You should know from trig that
    $$\sin^2 x = \frac{1-\cos 2x}{2}$$ Can you see how to get that result from
    $$\sin^2 x = -\frac{e^{i(2x)} + e^{-i(2x)} - 2}{4}$$using the hint I mentioned above.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier series help
  1. Fourier Series help (Replies: 7)

  2. Fourier series help (Replies: 1)

  3. Fourier Series Help (Replies: 3)

Loading...