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How to determine period of sinx

  1. Mar 5, 2012 #1
    How to determine period of sin and cos functions?
    I use:
    sin(x + p) = sin(x)
    => sin(x + p) - sin(x) = 0
    => 2*cos(x+p/2)*sin(p/2) = 0
    => either p/2 = k(pi) => p = 2k(pi)
    or x + p/2 = (2k+1)(pi)/2 => p = (2k+1)(pi) - 2x
    NOW I DON'T KNOW HOW TO FIND THE SOLUTION WHICH SATISFIES BOTH.. THOUGH I KNOW THAT PERIOD IS 2(PI) BUT I HAVE TO PROVE IT WITHOUT GRAPH.
     
  2. jcsd
  3. Mar 5, 2012 #2

    tiny-tim

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    Hi AAQIB IQBAL! :wink:
    Fine until here. :smile:

    Now that must be true for any x (for the same p) …

    which can only happen if sin(p/2) = 0. :wink:

    (in other words: you can ignore the other part)
     
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