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Periodic functions

  1. May 19, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the fundamental period of the expression sinx/sinx.can you guys please illustrate how to make its graph?

    2. Relevant equations
    Okay I know drawing graph can give me the period.Can the period be found by any other method?

    3. The attempt at a solution
    I'm told that the answer is pi. That is pi radians.I don't know how to sketch it's graph
     
  2. jcsd
  3. May 19, 2016 #2

    Math_QED

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    What exactly do you mean? f(x) = sinx/sinx is a constant function without the points for which sinx = 0.
     
  4. May 19, 2016 #3
    It's period is pi that's all I know about it and here is a key the period of cosx/cosx is also pi
     
  5. May 19, 2016 #4

    Math_QED

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    what is cosx/cosx equal to?
     
  6. May 19, 2016 #5

    RUber

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    The definition of a period is the smallest number n such that f(x+n) = f(x), right?
    If you look at ##f(x) = \frac{\sin x}{\sin x}## you should see what Math_QED was referring to...for all points where this function is defined, it can be simplified to a constant. However, there are places where the denominator is equal to zero and so f(x) at these points is undefined.
    You will notice that there is a regular spacing between these holes in the function. Use that as your period.
     
  7. May 19, 2016 #6
    Okay so you mean y=sinx/sinx will be equal to one but holes will appear at x=0 and pi, 2pi...... npi?
    And the spacing bw these holes gives me the period as 1? And same for cos? It will be undefined at npi/2?
     
  8. May 19, 2016 #7

    SammyS

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    No. It gives a period of π .
     
  9. May 20, 2016 #8
    Yeah I got it. It was a typo. Thanks guys and I really loved RUber's answer that made it crystal clear to me thanks bro
     
  10. May 20, 2016 #9
    Okay another question.. What is the lcm of pi, 2pi and pi/3?
     
  11. May 20, 2016 #10

    RUber

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    Lowest common multiple can't be smaller than the largest member of the group. Check that one first.
     
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