Trigonometry Help: Model Daylight Hours in Lowell, MA 2020

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SUMMARY

The discussion focuses on modeling daylight hours in Lowell, MA for the year 2020 using a sinusoidal function based on data from sunrise-sunset.org. Key calculations include determining the amplitude, vertical shift (midline), horizontal stretch (coefficient of the input variable), and horizontal shift (phase shift). Participants are encouraged to reference page 463 of their textbook for guidance on these calculations. A comparison between the model's output and actual daylight data is also required, along with graphical representations of the findings.

PREREQUISITES
  • Understanding of sinusoidal functions and their properties
  • Familiarity with the concepts of amplitude, vertical shift, and phase shift
  • Basic skills in using graphing calculators or spreadsheet software
  • Access to the website sunrise-sunset.org for data retrieval
NEXT STEPS
  • Learn how to calculate the amplitude and vertical shift of sinusoidal functions
  • Research methods for determining horizontal stretch and phase shift in trigonometric models
  • Explore graphing techniques using graphing calculators or software like Desmos
  • Study real-world applications of sinusoidal models in seasonal data analysis
USEFUL FOR

Students studying trigonometry, educators teaching mathematical modeling, and anyone interested in applying sinusoidal functions to real-world data analysis.

mcdwog
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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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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?
 

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