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.

A. Identify the independent and dependent variables, both with letter names and y and what they represent in this scenario.

Answer 1

The independent variable, time in months, is denoted by 't', and the dependent variable, precipitation in inches, is represented by 'P'. February's 2.25 inches of precipitation alongside an average of 3.5 inches assist in forming the parameters of the trigonometric function modeling Chicago's precipitation.

Step-by-step explanation:

When modeling precipitation in Chicago using a trigonometric function, the independent variable is represented by the letter t, which stands for time in months elapsed since the beginning of the year.

Here, January is 0, February is 1, and so on. The dependent variable is represented by the letter P (precipitation), which denotes the precipitation in inches.

February, being the driest month with 2.25 inches of precipitation, can be used to help determine the amplitude, phase shift, and vertical shift of the trigonometric function in relation to the average monthly precipitation of 3.5 inches.