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Periods of Trigonometric Functions

  1. Jan 23, 2005 #1
    Here are two general questions

    How would you find the period of:

    sin(2Pi*t)+sin(4Pi*t)

    or

    cos(3t)sin(2t)

    Thanks
     
  2. jcsd
  3. Jan 28, 2005 #2
    The first is simple it is one period of the lower frequency ( the other is a simple harmonic ) . In the second did you really mean multiply or just leave out a + sign??
    I do not always find the maths simple --- my fall back to this ( to get a clue ) is to graph the function. ( But not by hand ) .
    I always use QBasic in which you can set up the equations and the graph in a matter of minutes .
    However cos(a).cos(b) == a function of a+b and a-b so one frequency is 5 and the other 1 , so the frequency compared to either of the originals is 1.
    That is, due to multiplication beats are formed between two frequencies
    Since the normal wave equation is A.Sin ( 2.pi/T.t) it , means that 2.pi/T=1
    so T = 2.pi
    To solve these equations for T -- first compare them to the usual equation

    The multiplier of t is 2.pi.f for a simple wave or 2.pi/T --- then if required use the normal trig relations for compound functions .
    In cases of addition of sine waves there will only be a common period if the frequencies have an integer relation.
    The same is true for multiplications . In general there may be no period at all, or maybe extremely long. For instance cos(99.t).cos(101.t) will will have a period about 50x times greater than either .
    Ray.
     
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