In a certain town, the longest day of the year, which is in June, lasts fourteen hours. The shortest day of the year, which is in December, lasts ten hours. Twice per year, in March and September, the day is the same length as the night, or twelve hours.

Length of day varies sinusoidally through the year. Write an equation for H(m), the length of the day in hours, as a function of the cosine of m, the number of months since January.

Question

In a certain town, the longest day of the year, which is in June, lasts fourteen hours. The shortest day of the year, which is in December, lasts ten hours. Twice per year, in March and September, the day is the same length as the night, or twelve hours.

Length of day varies sinusoidally through the year. Write an equation for H(m), the length of the day in hours, as a function of the cosine of m, the number of months since January.

mlparks13 · Answer

Sorry this is too hard for me

yellowfellow007 · Answer

well first establish what amplitude would be? At the max it would have be 14 min would be 10.

yellowfellow007 · Answer

y=A*cos(Bx+C)+D

danjs · Answer

It says in june, the sixth month, the day is longest at 14 hrs, that is the middle point. It also says the minimum is 10 in month 12 december, those are the two endpoints. The graph is smooth curve between th epoints
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