Understanding Trigonometric Graphs

The video tutorial explains how to analyze a trigonometric function graph by determining its amplitude, period, phase shift, vertical shift, and midline. It starts by identifying the cycle of the graph and comparing it to the basic cosine function. The tutorial then discusses the vertical shift and confirms there is no phase shift. Finally, it calculates the amplitude by examining the distance between the maximum and minimum values relative to the midline.

What is the first step in analyzing a trigonometric graph?

• Determine the amplitude

• Identify the period

• Focus on a specific part of the graph

• Calculate the phase shift

How many units is the period of the given trigonometric function?

• 8 units

• 10 units

• 6 units

• 4 units

What is the period of the basic cosine function in radians?

• 0 to 4π radians

• 0 to 3π radians

• 0 to π radians

• 0 to 2π radians

What is the vertical shift of the given graph compared to the basic cosine function?

• Left 2 units

• Up 2 units

• Down 2 units

• Right 2 units

Does the given graph have a phase shift?

• Yes, it is shifted up

• Yes, it is shifted left

• Yes, it is shifted right

• No, there is no phase shift

What is the amplitude of the basic cosine function?

• 1

• 3

• 0.5

• 2

How is the amplitude of a trigonometric function determined?

• By the phase shift

• By the period of the function

• By the total distance from maximum to minimum

• By the distance from the midline to the maximum or minimum

What is the amplitude of the given graph?

• 4

• 1

• 2

• 3

What is the midline of the basic cosine function?

• y = 0

• y = 2

• y = -1

• y = 1

What is the midline of the given graph?

• y = 1

• y = 0

• y = 2

• y = 3