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Real-World Applications of Trigonometric Functions, Page 4

Modeling the Length of Day: Example

The following is another example using sinusoidal functions in modeling the length of any given day in an area of the world.

The length of a day in Cleveland, OH is given by the sinusoidal function: 

f(t) = 12 + 2.5 sin((2pi/365)t - 1.34)

f(t) is the number of hours of daylight on any given day of the year, t.

How many hours of daylight are there on the 10th day of the year?

If t =10: 

f(t) = 12 + 2.5 sin((2pi/365)10 - 1.34); f(t) = 12 + 2.5 sin(20pi/365 - 1.34); f(t) = 12 + 2.5 sin(-1.17); f(t) = 12 - 2.3; f(t) is approximately 9.7

There are approximately 9.7 hours of daylight on the 10th day of the year in Cleveland, OH.