Question

Suppose that the precipitation in Chicago can be modeled by a trigonometric function. Represent time in months elapsed since the beginning of the year (in other words, in January = 0; February = 1). The average monthly precipitation for the year is 3.5 inches, and February is the driest month of the year with 2.25 inches of precipitation. Find the amplitude and period of the function.

Answer 1

To find the amplitude and period of the trigonometric function that models the precipitation in Chicago, we need to determine the maximum and minimum values of the function and the length of one complete cycle. Given that the average monthly precipitation is 3.5 inches and February is the driest month with 2.25 inches, we can deduce that the maximum value is 3.5 inches and the minimum value is 2.25 inches. The amplitude is (3.5 - 2.25) / 2 = 0.625 inches. The period of the function requires additional information.

Step-by-step explanation:

To find the amplitude and period of the trigonometric function that models the precipitation in Chicago, we need to determine the maximum and minimum values of the function and the length of one complete cycle. Given that the average monthly precipitation is 3.5 inches and February is the driest month with 2.25 inches, we can deduce that the maximum value is 3.5 inches and the minimum value is 2.25 inches. The amplitude is half the difference between the maximum and minimum values, so the amplitude is (3.5 - 2.25) / 2 = 0.625 inches.

The period of a trigonometric function is the length of one complete cycle. In this case, the cycle represents the time it takes for the precipitation pattern to repeat. Since time is represented in months elapsed since the beginning of the year, the period will be the number of months it takes for the precipitation pattern to repeat. We will need more information to determine the period of the function.