Trigonometry Help: Model Daylight Hours in Lowell, MA 2020

In summary, the conversation was about using data from the website sunrise-sunset.org/us/lowell-ma to build a model (a sinusoidal function) that outputs the number of hours of daylight in Lowell for any given date in 2020. The model would need to find the amplitude, vertical shift, horizontal stretch, and horizontal shift. The dialogue also mentioned comparing the output of the model to the data from the website and providing a graph of the function. The conversation also mentioned using an example from page 463 of a textbook to find these values.
  • #1
mcdwog
2
0
Use the data from the website sunrise-sunset . org / us / lowell-ma to build a model (a sinusoidal function) whose output is the number of hours of daylight in Lowell when the input is the ordinal date (1 though 366) of the year 2020. Find (and show your calculations for finding): Amplitude Vertical Shift (Midline) Horizontal stretch (coefficient of the input variable, determined by the period) Horizontal Shift (Phase Shift) There is an example of how to find these on page 463 of your textbook. Use the model to show the hours of daylight on your birthday (or some other chosen day, if you prefer). Show the comparison between the output of your model and the datum from the website. Provide a graph of the function. This can be a picture of your calculator screens (one showing the y= screen, one showing the Window screen and one showing the graph). If you choose to provide a hand drawn graph, be sure to label the axes and all significant points.
 
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  • #4
Beer induced query follows.
mcdwog said:
... There is an example of how to find these on page 463 of your textbook. ...
What textbook are you referring to?
 

1. How is trigonometry used to model daylight hours in Lowell, MA 2020?

Trigonometry is used to model daylight hours in Lowell, MA 2020 by using the concept of the Earth's rotation and its position relative to the sun. The angles and distances between the Earth, sun, and Lowell, MA can be calculated using trigonometric functions, allowing us to determine the amount of daylight that will be received in a specific location.

2. What data is needed to model daylight hours using trigonometry in Lowell, MA 2020?

To model daylight hours using trigonometry in Lowell, MA 2020, we need data such as the latitude and longitude of the location, the date and time, and the tilt of the Earth's axis. This information is used to calculate the angle of the sun's rays and the length of the day.

3. How accurate is the trigonometric model for daylight hours in Lowell, MA 2020?

The trigonometric model for daylight hours in Lowell, MA 2020 is highly accurate, with a margin of error of only a few minutes. This is because trigonometry is based on precise mathematical calculations and takes into account the Earth's rotation and position relative to the sun.

4. Can trigonometry be used to predict daylight hours in other locations besides Lowell, MA 2020?

Yes, trigonometry can be used to predict daylight hours in other locations besides Lowell, MA 2020. As long as the necessary data is available, such as the latitude and longitude, the date and time, and the tilt of the Earth's axis, the same trigonometric principles can be applied to model daylight hours in any location.

5. Are there any limitations to using trigonometry to model daylight hours in Lowell, MA 2020?

One limitation of using trigonometry to model daylight hours in Lowell, MA 2020 is that it assumes a perfectly spherical Earth and a constant tilt of the Earth's axis. In reality, the Earth is not a perfect sphere and its axis can vary slightly, which may result in a small margin of error in the calculations.

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