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In this 6 page application or project activity, groups of students use their knowledge of sinusoidal functions to determine the functions that model the hours of daylight over a year. Cities around the world are explored, both on the same longitude and then same latitude to see how the sinusoidal function changes.
Students must determine the period (year), sinusoidal axis, amplitude and the horizontal translation (phase shift) necessary to determine the model. Toronto is used as the first example, with students determining other cities in the same latitude and longitude and then determining the function for each city.
Graphs are drawn, longest and shortest days are found.
Sinusoidal regression is also done. (It is assumed students are familiar with linear or quadratic regressions already)
Comparisons are made between the degree measure function students determined and the radian measure function that the calculator completed.
Groups of 2-3 work the best, but individual projects are also possible. There is a short individual assignment included to evaluate individual understanding
A brief rubric for both is also included. (Graphs worth xx pts, regression worth xx pts..) The answer file is 16 pages, including the original document, brief answers in the document and then the graph and tables of data.
Answers are provided, but not for all possible cities, as too many combinations could occur. Toronto calculations are completed. Data is shown for Orlando, Panama and Toronto.
A preview of pages 1 and 5 is available.
See my other application topics in Making Math Matter MMM as I am currently uploading several.