Sinusoidal Function Project (PC)

In this task, we gather and examine a periodic data set that can be modelled well with a sinusoidal function.

You may submit your project as a google doc/word document; a google slides file or as a poster. It should contain the following elements:

Page 1: A Title page with a short paragraph that summarizes the project.

Page 2: The data set (as a table – google sheet?) along with the source of the data set.

Page 3. A screen shot of the data points plotted, axes labelled, good choice of axes.

Page 4: Calculations for parameters a, b, c and d to model your data points with the function f(x)=a\sin(b(x-c))+d or f(x)=a\cos(b(x-c))+d.

Page 5: A screen shot of your data with your calculated curve. Discussion of where your curve fits best, where it fits least. Quantify the error using units from the context of the data.

Page 6: Using the ‘fitsin’ tool. The graph and the equation.

Page 7: An informed discussion of the model in the context of the data. The domain, the range, interpolation, extrapolation, what the crest/trough represent, what positive/negative values represent etc.

This is the suggested outline and need not be adhered to strictly. What matters is organized work that has a central theme that develops logically through diagrams and commentary.

Ideas for data

  1. Compare the amount of daylight hours over a year in two latitudes – eg, in Victoria vs Iqaluit;
  2. Plot sunrise times for one year on the same graph as sunset times for one location;
  3. Compare average high with average low temperature for one location for a full year;
  4. Plot the percent visible of the face of the moon for four months;
  5. Find two famous ferris wheels, other than the London Eye, and compare height/duration on the same graph
  6. Mark a bike tyre with chalk. Track the height of the chalk above the ground when (a) the bike is in the lowest gear; when (b) the bike is in the highest gear; for one full rotation of the pedals.
  7. Compare volume displacement in one cylinder in two different car engines, when running at 2000 rpm.
  8. Breathing rhythms: obtain data for volume of air in lungs over time, compare during rest, during exercise.
  9. Take tide data for one day during a full moon, and from the same location during a new moon.
  10. Other tide data – eg, compare Victoria water height for two days with Bay of Fundy water height for the same two days.
  11. Race Rocks current speed data. Compare one day during a full moon and one day during a new moon.
  12. The angle of the sun above the horizon at noon every day for a year, in one location.
  13. Electricity bill over 365 days. This information is available as a spreadsheet from byhydro to the person who pays the electricity bill.

Here’s a bunch more ideas

Partner or Individual?

Should you choose to compare two related data sets (such as most of the ideas above), then you may submit one project between two. A comparison leads to interesting discussion. If going solo, its ok to have just one data set.

Discussion

Address the following in the discussion:

  • Technical details of the regression model – domain and range.
  • An overall opinion of whether or not the trend of the model is a good fit for the trend of the data, as anticipated by your context.
  • An example of an interval or point where the model fits the data quite well – how small does the error get?
  • An example of an interval or point where the model does not fit very well – how big does the error get?
  • An example of interpolation – use the model to predict an value within the data set.
  • An example of extrapolation – use the model to predict a value beyond the data set. Test this value against a real world value if possible.
  • One or two observations of your own: (eg, “I notice that…” or “I wonder …”) regarding your data set, your model and your context.

Assessment

Pages 1,2,3 Managing the data. [15 marks]

Looking for a sufficient; well managed; well presented & sourced data set, and a nicely presented and well labelled graph.

Pages 4&5 Translating the curve y=sin(x). [10 marks]

Looking for – clear discussion on how you arrive at the values a,b,c and d. We will use radian measure in this project.

Page 6 [5 marks]

Page 7 [10 marks]

Looking for a discussion relating the context to the math, using math vocabulary.

You may submit the project twice, feedback will be given on the first copy.

 

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