The number of hours of daylight in san diego when you input any day of the year. let t be the day of the year (from 1 to 365), determine the number of hours of sunlight, h, if you enter a value for t using a sine function. the average number of daylight hours is 12, and the maximum and minimums during the summer and winter respectively are 14.4 to 9.6 hours.

  H(d) = 12 +2.4·sin(2π(d-80)/365)

Step-by-step explanation:

The midline of the function is given as 12 hours.

The amplitude of the function is the difference between that and either peak:

  14.4 - 12 = 2.4 . . . . hours

The period is given as 365 days.

The function will cross the midline to larger values when the day number is 80 (the spring equinox), so that is the horizontal offset of the function to the right.

The function can be written as ...

  H(d) = midline + amplitude × sin(2π/period × (x - horizontal offset))

  H(d) = 12 + 2.4·sin(2π(x -80)/365)

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The graph shows the hours of daylight for days 172 (summer solstice) and 355 (winter solstice).