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!

Homework Help: Expanding sin4x

  1. Mar 25, 2009 #1
    Hey, i need help with a problem i'm having i'm not sure about an expansion

    1. The problem statement, all variables and given/known data

    Solve the following equation for -[tex]\pi[/tex]<[tex]\theta[/tex]<[tex]\pi[/tex]
    sin4[tex]\theta[/tex] = cos2[tex]\theta[/tex]
    I'm not sure about how to expand sin4[tex]\theta[/tex]

    2. The attempt at a solution
    I have tried putting sin4[tex]\theta[/tex] as sin(2[tex]\theta[/tex]+2[tex]\theta[/tex]) and expanding to get sin2[tex]\theta[/tex]cos2[tex]\theta[/tex] + cos2[tex]\theta[/tex]sin2[tex]\theta[/tex]. However it just becomes very messy, I was just wondering if i am doing this correctly as the answer i recieve is different to the one in my textbook
  2. jcsd
  3. Mar 25, 2009 #2
    Ever heard of: [tex]\sin 2\phi = 2\sin \phi \cos \phi[/tex] ?
  4. Mar 25, 2009 #3

    I remember having to do this same problem in my first year at uni, but i cant remember the exact method. You have to use something called De Moivre's formula (http://en.wikipedia.org/wiki/De_Moivre's_formula).

    Hope that helps,

  5. Mar 25, 2009 #4
    yeah, i get
    sin4x = 2sin2xcos2x and from then on i do
    i then carry on expanding and end up with 4sinxcos3x-4sin3xcosx
    im not sure how to carry on from there :confused:
  6. Mar 25, 2009 #5
    You don't need to keep on expanding. Substituting once gives you a [tex]\cos2\theta[/tex] term on both sides. You can cross those away (under certain conditions).
  7. Mar 25, 2009 #6
    so is it 2sin2x = 1 ? :)
  8. Mar 25, 2009 #7
    Yes, correct, but only when you are allowed to cross out the [tex]\cos 2\theta[/tex] term. Any idea when that move is not allowed..?
  9. Mar 25, 2009 #8
    not too sure is it when they are being added or subtracted?
  10. Mar 25, 2009 #9
    Be careful with your next move... ;)

    http://pix.motivatedphotos.com/2008/11/8/633617527281144116-dividebyzero.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  11. Mar 25, 2009 #10
    :P in the end i get sinxcosx =0.25 but in not sure how to get the answer out of it :P
  12. Mar 25, 2009 #11
    Stop expanding. The previous equation was as far as you needed to go. You have to know this one by heart: [tex]\sin 2\theta = \frac{1}{2}[/tex].

    Put differently, for what value of [tex]\phi[/tex] do we have [tex]\sin\phi=\frac{1}{2}[/tex]?

    If not, look it up ;)
  13. Mar 25, 2009 #12
    if i place that in my formula it doesn't give me the same answer as my text book though
    if sinx = 0.5 then 0.5cosx=1/4 then it gets cosx = .5
    this is pie/3 however the answers in my text book say pie/12 pie/4 etc
  14. Mar 25, 2009 #13


    User Avatar
    Homework Helper

    for sin2x=0.5 =>2x=pi/6 and the other angles in the range ( find what x equals to)

    for cos2x=0 => 2x=pi/2,other angles in the range you want (find x)

    combine these answers.
  15. Mar 25, 2009 #14
    I finally got it, thanks for the help everyone :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook