Modeling w/Trig Functions Homework

Front

What is the amplitude of a trigonometric function, and how is it determined?

Back

The amplitude of a trigonometric function is the maximum distance from the midline to the peak (or trough) of the graph. It is calculated as half the distance between the maximum and minimum values of the function.

Front

How do you find the vertical shift of a trigonometric function?

Back

The vertical shift is found by determining the midline of the function, which is the average of the maximum and minimum values. It represents the vertical displacement of the graph from the origin.

Front

What is the general form of a cosine function used to model periodic behavior?

Back

The general form of a cosine function is y = A * cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

What is the significance of the period in a trigonometric function?

Back

The period of a trigonometric function is the length of one complete cycle of the graph. It determines how frequently the function repeats its values.

Front

How do you determine the period of a sine or cosine function?

Back

The period of a sine or cosine function can be determined using the formula: Period = 2π / |B|, where B is the coefficient of x in the function.

Front

What does the initial population represent in a population model using trigonometric functions?

Back

The initial population represents the value of the function at t = 0, indicating the starting quantity of the population before any changes occur.

Front

How do you interpret the coefficients in a sine or cosine function modeling a real-world scenario?

Back

The coefficients in a sine or cosine function represent the amplitude (A), frequency (B), horizontal shift (C), and vertical shift (D), which together define the behavior of the modeled phenomenon.

Front

What is the maximum value of a population modeled by a sine function?

Back

The maximum value of a population modeled by a sine function is calculated as the vertical shift plus the amplitude, representing the highest point the population can reach.

Front

What is the minimum value of a population modeled by a sine function?

Back

The minimum value of a population modeled by a sine function is calculated as the vertical shift minus the amplitude, representing the lowest point the population can reach.

Front

How can you identify the range of a trigonometric function?

Back

The range of a trigonometric function can be identified by calculating the minimum and maximum values based on the vertical shift and amplitude.