How Does Daylight Vary by Month Using a Sinusoidal Function?

  • Thread starter Calixto
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In summary, the conversation discusses the number of hours of daylight at a person's home, which is approximated by the formula h = 12 + 4sin[2π/12(m-9)], where m represents the month. The conversation then asks how long the shortest day of the year is at the person's location and whether they live in the Northern or Southern Hemisphere. It is also noted that the number 12 appears twice in the formula for different reasons, and the real-world meaning of each 12 is explained. The conversation also briefly mentions how to find the minimum of a function and the minimum and maximum of sine in particular.
  • #1
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.
 
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  • #2
How does one usually find the minimum of a function?
 
  • #3
Also, how does one find the minimum and maximum of sine in particular?
 

1. What is a Daylight Sinusoid?

A daylight sinusoid is a mathematical model that represents the daily variation of sunlight intensity on Earth. It is a sinusoidal curve that shows the gradual increase and decrease of sunlight throughout the day, with the peak occurring at midday.

2. How is a Daylight Sinusoid helpful?

A daylight sinusoid is helpful in understanding and predicting the amount of sunlight available at different times of the day. It is also used in fields such as astronomy and ecology to study the effects of sunlight on various phenomena.

3. What factors affect the shape of a Daylight Sinusoid?

The shape of a daylight sinusoid is affected by various factors, including the Earth's rotation, axial tilt, and the position of the observer on the Earth's surface. Other factors such as atmospheric conditions and topography can also have an impact.

4. How is a Daylight Sinusoid calculated?

A daylight sinusoid is calculated using trigonometric functions, such as sine and cosine, which take into account the Earth's rotation and axial tilt. It can also be calculated using geographic coordinates and the date and time of day.

5. Are there any tools or resources available to help visualize a Daylight Sinusoid?

Yes, there are various online tools and software programs available that can generate visual representations of a daylight sinusoid. These can be helpful in understanding the concept and how it applies to different locations and times of the year.

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