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How would I solve this problem for t?
720 = 11.895+2.545sin [2pi/366(t-80.5)]

  • trig -

    same way you would solve for any equation. collect t stuff on one side, and work your way inside out the expressions till t ia all alone:

    708.105 = 2.545sin [2pi/366(t-80.5)]
    278.2338 = sin [2pi/366(t-80.5)]

    at this point you are stuck. sin(x) is never more than 1, so there is no way it can be 278.2338

    I suspect a typo somewhere.

  • trig -

    It is intuitively obvious that this equation cannot have a solution the way it was written

    the sin(anything) has to be a number between -1 and +1

    so if 720 = 11.895 + x , the value of x cannot possible fall between - 1 and +1

    check your typing, or if correctly typed, there is no solution

  • trig -

    i think i figured out my mistake. it should be

    720 = 713.7+152.7 sin [(2pi/366)(t-80.75)]

    this problem is modelling minutes of daylight in a town using the form y = d+a sin[b(t-c)]. let y equal 720 minutes of daylight and let t=the number of days in 2012

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