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Math Help - Bioryhtms equation

  1. #1
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    Bioryhtms equation

    Physical potential Period 23 days
    Emotional potential period 28 days
    Intellectual potential period 33 days

    If the equation determining each of your "potentials" is of the form

    P(t)= 50 sin (at) + 50 where t is days and a is a constant specific to each of your potentials and P(t) is your potential after t days expressed as a percentage

    How to find the value of a for each potential

    And how to determine when the three "potentials" are each at their peak of 100%

    when t=0 all potentials start at 50%

    Any help always appreciated
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  2. #2
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    Quote Originally Posted by delpin View Post
    Physical potential Period 23 days
    Emotional potential period 28 days
    Intellectual potential period 33 days

    If the equation determining each of your "potentials" is of the form

    P(t)= 50 sin (at) + 50 where t is days and a is a constant specific to each of your potentials and P(t) is your potential after t days expressed as a percentage

    How to find the value of a for each potential

    And how to determine when the three "potentials" are each at their peak of 100%

    when t=0 all potentials start at 50%

    Any help always appreciated
    To find a: Call the period of the cycle T. Then we know that one cycle corresponds to a time T. Thus
    2 \pi = a T

    a = \frac{2 \pi}{T}

    Each potential is at its peak when sin(at) = 1. So when
    at = \frac{\pi}{2}

    t = \frac{\pi}{2a}
    or, if you insert the value of a from the first part:
    t = \frac{\pi}{2 \frac{2 \pi}{T}} = \frac{T}{4}

    -Dan
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  3. #3
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    Extension to the question...

    Thank you. Muchly appreciated (again)

    What then would be the easiest way of determining when all three cycles reach their peak simultaneously?
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