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Homework Help: Trig inequality?

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that x=sin(piex) + cos(piex) has a solution in [0,-1]

    3. The attempt at a solution

    well i know that 0 <= x <= 1
    therefore 0 <= sin(piex) + cos(piex) <= 1

    But how do i go about solving this inequality?
  2. jcsd
  3. Oct 3, 2007 #2


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    Homework Helper

    You don't go about solving it. You just prove it has a solution. Change the equation into f(x)=x-sin(pi*x)-cos(pi*x)=0. f(0)=(-1). f(1)=2. Does that suggest anything?
  4. Oct 4, 2007 #3


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    That certainly is NOT true! What is sin(pi)+ cos(pi)? Look at the signs of sin(pix)+ cos(pix)- x at 0 and 1.
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