Sinusoidal Modeling: Real World Applications
Due:
Any variable that is cyclical or periodic can be modelled by a sinusoidal function.
There are many examples of periodic phenomena that are suitable for sinusoidal
modelling. Some examples include:
o Changes in temperature over time
o Hours of daylight over time
o Ocean wave heights (high and low tide) over time
o Amount of the moon visible each day of the month
o Changes in population size of predator-prey species, ex. the Canadian Lynx
and the Arctic Hare or the Moose and Wolf populations on Royal Island
Your Task
o You are to select a natural phenomenon that can be modelled sinusoidally -
you can use any listed above. If you want to research something else ask me
before you start.
o You must research and collect data on your chosen phenomenon – there are
many databases available online where you can access data
o You will need 24 data points
o You will need to graph the original data – you can use the desmos graphing
calculator for this, or excel if you are more comfortable with that
o Using your graph and data determine a predictive model in the form of y =
asin(k(x-d))+c or y = acos(k(x-d))+c
o Graph your predictive model – again desmos is useful for this.
o Compare the graph of the model to the original graph of the data –
similarities? differences?
o What would you need to make your model more accurate?
o Make a prediction using your model and compare it to the actual data – why
might they be different?
o What could the model you developed be used for? Try and come up with two
applications.