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Trig sums

  1. Jan 28, 2007 #1
    1. The problem statement, all variables and given/known data

    for what values of x is cos(x) - sin(x) < cox(x) + sin(x) where 0 =< x =< 2pi

    2. Relevant equations

    none.

    3. The attempt at a solution

    I actually drew out the funtions and added them.
    In my graphs, I get that:

    cos(x) - sin(x) < cos(x) + sin(x) for for 0 =< x =< pi

    When I try to show this in Matlab, i ger messy results?

    Any ideas?
     
  2. jcsd
  3. Jan 28, 2007 #2
    There's a simpler way to do it. Did you try algebraically manipulating the equation?
     
  4. Jan 28, 2007 #3
    no ... infact, im not sure what you mean?

    cos(x) - sin(x) < cos(x) + sin(x)
    cos(x) - cos(x) < sin(x) + sin(x)
    0 < 2sin(x)
    0 < sin(x)

    and sin(x) is bigger than zero for 0 =< x =<pi/2

    This dosn't seem right to me...
     
  5. Jan 28, 2007 #4
    Actually, sin(x)>0 everywhere on the open interval (0,pi).
     
  6. Jan 28, 2007 #5
    oh yeah, sorry, i got confused...

    so that means that cos(x) - sin(x) is less than cos(x) + sin(x) for (0,pi) ?
     
  7. Jan 28, 2007 #6
    Yes. 10char
     
  8. Jan 28, 2007 #7
    i don't like this because it dosn't match up with my graphs.

    but the math looks right, therefore, their must exist an error in my graphs.
     
  9. Jan 28, 2007 #8
    opps, it actually does match with my graphs... :)
     
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