INTRODUCTORY EXERCISES - Modeling with Trigonometric Functions

(1) What is the period of the earth's revolution around the sun?

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(2) A company in a northern climate has sales of skis as given by:

S(t) = 10[1 - cos(/6) t],

where t = time, in months since July 1, and S(t) is in thousands of dollars.
  1. Sketch a graph of the function over a 12-month interval [0,12].
  2. What is the period of the function?
  3. What is the minimum amount of sales and when does it occur?
  4. What is the maximum amount of sales and when does it occur?


(3) The angle of elevation to the top of the Empire State Building in New York is found to be 11o from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the Empire State Building.


(4) A pilot flying at an altitude of 1200 feet is starting his approach. He is 4500 feet along his flight path from the runway.

(a) What is his horizontal distance (x) from the runway?

(b) What is his angle of approach ()?


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