# Trigonometry

The number of hours of daylight in a city in the northern hemisphere shows periodic behavior over time.
- The average number of daylight hours is 12
- The maximum number of daylight hours is 14.4
- The period is 365 days
- The day with the least sunlight is december 20
which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year?

A) H(t)= -14.4 sin(0.017t)
B) H(t)= 14.4 sin(0.017t)
C) H(t)= -2.4 sin(0.017t) + 12
D) H(t)= 2.4 sin(0.017t) + 12

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1. the amplitude is the max - average = 2.4
so, start out with

H(t) = 12+2.4sin(kt)

the period is 265, so k = 2pi/365 = 0.017

H(t) = 12+2.4sin(0.017t)

since the minimum is at t=0, we want

H(t) = 12-2.4cos(0.017t)

Not a choice, unless there is a typo and you want (C)

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2. Yes, I'm very sorry, the last two are meant to be cos, and I was debating whether it was C or D, thank you for your help!:)

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3. What was the answer to this question?

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4. 13

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