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Two consecutive days of the week experience a maximum temperature of 90 degrees F at 1:00pm and a minimum temperature of 44 degrees F at 1:00am. Write a cosine equation measured in house that would model this behavior. Let x=0 represent 1:00pm on the first day.

  • calculus -

    since the range is 44-90, the amplitude is (90-44)/2 = 23

    The period is 24 hours, so

    t = 23cos(2pi/24 x)+67

    t(0) = 23cos(0)+67 = 23+67 = 90
    t(12) = 23cos(2pi/24 * 12)+67 = 23cos(pi)+67 = -23+67 = 44

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