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Determining the period of a trigonometric function

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data

    $$f(x)=sin2x+cos4x$$

    2. Relevant equations


    3. The attempt at a solution

    $$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$
     
  2. jcsd
  3. Oct 17, 2013 #2
    What is the lowest common multiple of the periods of sin2x and cos4x ?
     
  4. Oct 17, 2013 #3

    arildno

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    Suppose you have two periods, p_1 and p_2
    the COMMON period must then satisfy n*p_1=m*p_2, for integers n and m to be determined.

    That is, the common period must be, as Tanya Sharma says, a COMMON MULTIPLE of the two periods, and the LEAST one at that. :smile:
     
  5. Oct 17, 2013 #4
    How does that work considering that cos is sin but displaced on the x-axis?

    According to this graph, T=pi is wrong:

    eZclCyl.png
     
  6. Oct 17, 2013 #5
    Never mind.

    I'm an idiot. You're right.

    Thanks.
     
  7. Oct 17, 2013 #6

    arildno

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    No,it isn't.

    Look at the respective function values of sin(2x) and cos(4x) at two x's a pi apart.

    BOTH functions repeat THEMSELVES here, whether you use -pi/3 and 2pi/3 or "0 and pi" or whatever other couple of x's.

    The common period of two functions does NOT mean that they equal each other at those points.
     
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