Answer:
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).
