Modeling Periodic Phenomena with Trigonometric Functions

This video tutorial covers the modeling of periodic phenomena using trigonometric functions. It begins with an introduction to the general forms of sine and cosine equations and their transformations. The tutorial explains how these transformations affect the graphs vertically and horizontally. It also discusses the use of trigonometric models in real-world applications, such as temperature prediction and daylight modeling. The video concludes with examples of modeling daylight hours in Denver using sinusoidal functions.

What effect does the parameter 'A' have on the graph of a trigonometric function?

• It shifts the graph horizontally.

• It shifts the graph vertically.

• It stretches or shrinks the graph vertically.

• It changes the period of the graph.

How does the parameter 'B' affect the period of a sine or cosine function?

• It determines the period as 2π/B.

• It doubles the period.

• It halves the period.

• It has no effect on the period.

Which trigonometric function has a period of π?

• Secant

• Tangent

• Sine

• Cosine

What is the purpose of using a five-point pattern when graphing sine and cosine functions?

• To determine the amplitude

• To simplify the graphing process

• To find the period

• To calculate the phase shift

What is the amplitude of the temperature model for New Orleans described in the lesson?

• 4

• 8

• 12

• 16

How many hours of daylight does Denver experience on the longest day of the year?

• 15 hours

• 12 hours

• 9 hours

• 18 hours

In the context of trigonometric models, what does the variable 'k' typically represent?

• The frequency

• The vertical shift

• The horizontal stretch

• The phase shift