How Does Daylight Vary by Month Using a Sinusoidal Function?

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SUMMARY

The discussion centers on the sinusoidal function representing daylight hours, expressed as h = 12 + 4sin[2π/12(m-9)], where m denotes the month. The shortest day of the year occurs in December (m=12), yielding approximately 8 hours of daylight. The person lives in the Northern Hemisphere, as the formula is structured to reflect seasonal variations typical of this region. The two occurrences of the number 12 in the formula represent the average daylight hours and the periodicity of the sine function, respectively.

PREREQUISITES
  • Understanding of sinusoidal functions
  • Knowledge of trigonometric concepts, specifically sine
  • Familiarity with periodic functions and their applications
  • Basic knowledge of seasonal daylight variations
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Students of mathematics, educators teaching trigonometry, and anyone interested in understanding seasonal changes in daylight hours through mathematical modeling.

Calixto
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Daylight sinusoid any help appreciated :)

A person finds that the number of hours of daylight at his home is approximately given by

h = 12 + 4sin[2π/12(m-9)]
where m represents the number of the month (January = 1, February = 2, etc.)

a) At the person's location, how long is the shortest day of the year?

b) Does the person live in the Northern or Southern Hemisphere?

c) The number 12 occurs twice in the formula, but for two different reasons. Explain the real world meaning of each of the 12's.
 
Physics news on Phys.org
How does one usually find the minimum of a function?
 
Also, how does one find the minimum and maximum of sine in particular?
 

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