Modeling with Trigonometric Functions

The video tutorial explains how to model real-world phenomena using sine and cosine functions. It covers the generic form of a trigonometric function model, including how to calculate amplitude, midline, phase shift, and period. The tutorial provides a step-by-step guide to finalizing a function model with all necessary parameters, using a practical example to illustrate the process.

What is the primary focus of the video on modeling?

• Modeling with quadratic functions

• Modeling with linear functions

• Modeling with sine and cosine functions

• Runway modeling

Why are sine and cosine functions used in modeling?

• They are exponential functions

• They are periodic functions

• They are quadratic functions

• They are linear functions

What is the generic form of a trigonometric function used for modeling?

• y = mx + b

• y = ax^2 + bx + c

• y = e^x

• y = A sin(Bx - C) + D

What must be filled in to have a functioning trigonometric model?

• The values of A, B, C, and D

• The values of x and y

• The values of m and b

• The values of a, b, and c

How is the amplitude of a trigonometric function determined?

• By finding the maximum value

• By finding the minimum value

• By calculating half the distance between the maximum and minimum values

• By adding the maximum and minimum values

What is the amplitude if the maximum is 66 and the minimum is 41?

• 12.5

• 25

• 15

• 22.5

What does the midline of a trigonometric function represent?

• The minimum value

• The maximum value

• The average of the maximum and minimum values

• The x-axis

How do you calculate the midline value?

• By multiplying the maximum and minimum

• By dividing the maximum by the minimum

• By adding the maximum and minimum and dividing by 2

• By subtracting the minimum from the maximum

What is the phase shift in a trigonometric function?

• The period

• The horizontal shift

• The amplitude

• The vertical shift

How is the phase shift determined?

• By finding the starting point of the sine curve

• By finding the ending point of the sine curve

• By calculating the amplitude

• By calculating the period