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: Solve Sin6x+sin4x

  1. May 6, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]sin6x+sin4x=0[/tex]

    2. Relevant equations

    [tex]sinx=2sin\frac{x}{2}cos\frac{x}{2}[/tex]

    [tex]sin2x=2sinxcosx[/tex]

    [tex]cos2x=cos^2x-sin^x[/tex]

    3. The attempt at a solution

    [tex]2sin3xcos3x+2sin2xcos2x=0[/tex]

    [tex]sin3xcos3x+sin2xcos2x=0[/tex]

    What shall I do next?
     
  2. jcsd
  3. May 6, 2008 #2

    Defennder

    User Avatar
    Homework Helper

    What exactly are you suppose to do? What is the question?

    EDIT: Is it to solve for x?
     
  4. May 6, 2008 #3
    Yes. I need to find x.
     
  5. May 6, 2008 #4
    Ohh... Can I solve it like this:

    [tex]sin6x=-sin4x[/tex]

    [tex]sin6x=sin(-4x)[/tex]

    [tex]6x=-4x+2k\pi[/tex]

    [tex]10x=2k\pi[/tex]

    [tex]x=\frac{k\pi}{5}[/tex]

    ??
     
  6. May 6, 2008 #5

    Defennder

    User Avatar
    Homework Helper

    That is partially correct. But you're missing out on other possible values of x. [tex]x=\frac{\pi}{2} [/tex] also satisfies the equation but it's not expressible in your answer.

    Use this trigo identity:
    [tex]2sin(Ax)cos(Bx) = sin((A-B)x) + sin((A+B)x)[/tex]
     
  7. May 6, 2008 #6
    Yes I forgot.

    [tex]6x=\pi+4x+2k\pi[/tex]

    [tex]x=\frac{\pi}{2}+k\pi[/tex]
     
  8. May 6, 2008 #7

    Defennder

    User Avatar
    Homework Helper

    Where did pi in your first equation come from?
     
  9. May 6, 2008 #8
    Remember this:

    x=arcsinx+2kpi

    x=pi - arcsinx + 2kpi

    ?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook