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Time and Temperature

Part 4: Summary

The following questions refer to a sinusoidal function of the form

y(t) = A + B sin [ C (t - t0)].

  1. How is A related to the average value of y(t)? How is A related to the largest and smallest values of y(t)?
  2. How is B related to the largest and smallest values of y(t)?
  3. How is C related to the period of the function?
  4. How do you determine the offset t0?
  5. If you know the largest and smallest values of y, as well as the period, how can you determine all four coefficients?
  6. What would you expect to be the period of an hours-of-sunlight function? Why?
  7. What would you expect to be the period of a long-term-average temperature function? Why?
  8. Some of the data sets studied in this module were not fit very well by sinusoids. Which ones, and what was wrong with the fit?
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Last modified: October 28, 1997