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Graph troubles

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data
    express cos^4 x in terms of cos 4x and cos 2x given that

    cos^ x = 0.5(1 + cos 2x)


    3. The attempt at a solution

    i did some playing around for a minute and came to this;

    cos^4 x = 0.25 + (cos2x)/2 + (cos 4x +1)/8

    and thought, great! now i'll just check it on wolfram however i got this;

    http://www.wolframalpha.com/input/?i=y+=0.25+++(cos2x)/2+++(cos+4x++1)/8

    as opposed to

    http://www.wolframalpha.com/input/?i=cos+^4+x

    now, just looking at the graphs it seems okay however none of the alternate forms or expansions are the same, i would love it if someone could just verify that i'm right it's quite an important question!

    thanks again
     
  2. jcsd
  3. Sep 19, 2009 #2
    your answer is correct

    if you group everything over a common denominator it might become more apparent
     
  4. Sep 19, 2009 #3
    thanks alot for that, it was really bugging me :D
     
  5. Sep 19, 2009 #4

    VietDao29

    User Avatar
    Homework Helper

    You can always try to graph as a way to check your work:

    [tex]y = \cos ^ 4 x - \left( 0.25 + \frac{\cos (2x)}{2} + \frac{\cos(4x) + 1}{8} \right)[/tex]

    to see if it turns out to be the x axis. If it does, then, everything should be fine. :)

    Btw, your expression can be further simplified to:

    [tex]\cos ^ 4 x = {\color{red}\frac{5}{8}} + \frac{\cos (2x)}{2} + \frac{\cos(4x)}{8}[/tex]
     
  6. Sep 19, 2009 #5
    I got
    [tex]\cos ^ 4 x = {\color{red}\frac{3}{8}} + \frac{\cos (2x)}{2} + \frac{\cos(4x)}{8}[/tex]
     
  7. Sep 19, 2009 #6
    that's a good idea actually, thanks

    i'm sure he meant 3/8
     
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