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Success in business depends on many factors. Buying habits of consumers, trends in fashion and taste, seasonal trends, the strength of the competition, and the condition of the national and international economies all affect the fortunes of a business. The result of these factors is that businesses often show a broad overall pattern of growth or decline superimposed on a continuing series of small ups and downs. Such business cycles can often be modeled by using trigonometric functions. Recall that sinusoidal trigonometric functions are periodic.

The economist for a large sporting-goods manufacturer developed the following function to model the company's sales, where S is sales in millions of dollars and t is the week of the year, beginning January 1 of each year:

S = 8 + t/52 – 6cos(πt/26)
Which of the following terms in the equation increases as t increases?


  • precalc -

    you know that cos(u) might either decrease or increase, depending on u.

    surely t/52 increases when t does.


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