ADVANCED EXERCISES-Modelling with Trigonometric Functions

(1) A patient in the hospital had an illness in which his temperature (in degrees Celsius) varied from a low of 37o to a high of 40.4o. The length of time between successive highs is 16 days.

  1. Determine the formula for the temperature, T, of the patient at time t in days since the beginning of the illness. Assume that the function describing the temperature can be modeled with a sine function, with no phase shift.
  2. Sketch a graph of the function over the interval 0 t 20.
  3. According to this model, what was the patient's original temperature?
  4. What is the patient's temperature on day 4 of his illness?
  5. When does the first temperature high occur? 
HINT: You can determine the period using the time between successive highs.  And the low and high temperatures tell you what the "vertical center" of the temperature function is, as well as the amplitude.



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