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; February). The average monthly precipitation for the year is [average inches], and February is the driest month of the year with [February inches] of precipitation.

a. Identify the independent and dependent variables, both with letter names (and) and what they represent in this scenario.

Answer 1

Final answer:

The independent variable, represented by the letter 't,' stands for time in months elapsed since the beginning of the year. The dependent variable, denoted by 'P(t),' symbolizes the amount of precipitation in inches.

Step-by-step explanation:

In this scenario, the independent variable 't' signifies time in months since the start of the year, ranging from 0 (January) to 11 (December). Meanwhile, the dependent variable 'P(t)' represents the monthly precipitation in inches. Considering a trigonometric function to model precipitation, the specific equation might incorporate sine or cosine functions that oscillate throughout the months, capturing the seasonal fluctuations in precipitation. By analyzing the provided data of the average annual precipitation and the lowest precipitation in February, one could develop a trigonometric function that aligns with these values, perhaps involving amplitude, phase shifts, or offsets to accurately model Chicago's precipitation pattern over the months.

Understanding the trigonometric behavior of functions assists in representing natural periodic variations, which could mirror the seasonal changes in precipitation. Using these mathematical functions allows for predictions and analysis of patterns that help in various applications, including climate studies and resource management.

Answer 2

The independent variable, represented by the letter 't,' stands for time in months elapsed since the beginning of the year. The dependent variable, denoted by 'P(t),' symbolizes the amount of precipitation in inches.

Explanation:

In this scenario, the independent variable 't' signifies time in months since the start of the year, ranging from 0 (January) to 11 (December). Meanwhile, the dependent variable 'P(t)' represents the monthly precipitation in inches. Considering a trigonometric function to model precipitation, the specific equation might incorporate sine or cosine functions that oscillate throughout the months, capturing the seasonal fluctuations in precipitation.

By analyzing the provided data of the average annual precipitation and the lowest precipitation in February, one could develop a trigonometric function that aligns with these values, perhaps involving amplitude, phase shifts, or offsets to accurately model Chicago's precipitation pattern over the months.

Understanding the trigonometric behavior of functions assists in representing natural periodic variations, which could mirror the seasonal changes in precipitation. Using these mathematical functions allows for predictions and analysis of patterns that help in various applications, including climate studies and resource management.