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Math Help - Periodic Functions

  1. #1
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    Periodic Functions

    Is sin(7t) + 2sin(10t) Periodic, if yes what is the period or angular frequency?

    Is cos(2t) + cos ( 2 * pi * t) Periodic?

    How exactly can we tell if a function is periodic without graphing it?

    Thanks in advance.
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  2. #2
    Member HappyJoe's Avatar
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    sin(7t) is periodic with period 2pi/7 while 2sin(10t) is periodic with period 2pi/10. The smallest number, which is a multiple of both periods, that is, of 2pi/7 and 2pi/10, is 2pi, which is then the period of the sum.

    For the other problem, cos(2t) has period pi, while cos(2pi*t) has period 1. There is no number, which is an integer multiple of both of these periods, so the function cos(2t) + cos(2pi*t) is not periodic.
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  3. #3
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    Thanks dude, I appreciate it. That actually cleared everything up (:
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