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: 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




Loading...