Understanding Trigonometric Graph Periods

The video tutorial explains the concept of periods in trigonometric graphs, focusing on sine and cosine functions. It uses the unit circle to illustrate how these graphs repeat their values over a cycle of 2π. The tutorial also covers the concept of co-terminal angles and demonstrates how to calculate the period using the standard form of trigonometric functions. Examples are provided to show how transformations affect the period, emphasizing the role of the variable B in the standard form.

What is the period of a standard sine or cosine graph?

• π

• 2π

• π/2

• 4π

How is the period of a trigonometric graph defined?

• The time it takes for the graph to reach its maximum value

• The distance it takes for the graph to start repeating its values

• The distance it takes for the graph to complete one full cycle

• The time it takes for the graph to reach its minimum value

What is the period of y = sin(x)?

• π/2

• 2π

• 4π

• π

What is the period of y = cos(x)?

• π

• 4π

• 2π

• π/2

What tool is used to evaluate the period of sine and cosine graphs?

• Ruler

• Protractor

• Unit circle

• Graphing calculator

What is the cosine value at an angle of π/4 on the unit circle?

• 1/2

• 1

• 0

• √2/2

What are co-terminal angles?

• Angles that have the same initial side

• Angles that are multiples of π

• Angles that are multiples of 2π

• Angles that have the same terminal side

What happens to the cosine graph when you add 2π to an angle?

• The graph shifts vertically

• The graph shifts horizontally

• The graph repeats itself

• The graph becomes undefined

At what angle does the cosine graph return to its starting point?

• 3π

• 2π

• 4π

• π

What is the standard form of a sine function?

• y = a * sin(BX - C) + D

• y = a * cos(BX - C) + D

• y = a * tan(BX - C) + D

• y = a * cot(BX - C) + D