Transformations of Trigonometric Functions

This tutorial covers transformations of trigonometric graphs, focusing on sine, cosine, and tangent functions. It explains how to apply translations parallel to the x-axis by modifying the function's input. The video provides examples and exercises for each type of graph, demonstrating how to shift the graphs left or right by specific degrees. By the end, viewers should understand how to apply these transformations to any trigonometric graph.

What are the standard trigonometric graphs discussed in this tutorial?

• y = sin x, y = cos x, y = cot x

• y = sin x, y = cos x, y = tan x

• y = sec x, y = csc x, y = tan x

• y = sin x, y = sec x, y = tan x

What does the transformation y = f(x - Alpha) represent?

• A vertical shift

• A horizontal shift

• A reflection

• A scaling

In the transformation y = f(x - 45), what does the 45 represent?

• A vertical shift

• A scaling factor

• A horizontal shift to the right

• A horizontal shift to the left

How does the sine graph change when transformed by y = f(x - 45)?

• Shifts 90 degrees to the right

• Shifts 90 degrees to the left

• Shifts 45 degrees to the right

• Shifts 45 degrees to the left

In the transformation y = f(x - 45), what is the direction of the shift?

• Left

• Right

• Down

• Up

In the transformation y = f(x - 45), what is the direction of the shift?

• Left

• Down

• Right

• Up

What is the effect of the transformation y = f(x + 90) on the sine graph?

• Shifts 90 degrees to the right

• Shifts 90 degrees to the left

• Shifts 45 degrees to the right

• Shifts 45 degrees to the left

When transforming y = f(x + 90), what is the value of Alpha?

• 90

• -90

• 45

• -45

What happens to the sine graph when transformed by y = f(x - 90)?

• Shifts 45 degrees to the left

• Shifts 45 degrees to the right

• Shifts 90 degrees to the left

• Shifts 90 degrees to the right

What is the transformation effect of y = f(x + 90) on the sine graph?

• Shifts 45 degrees to the right

• Shifts 90 degrees to the left

• Shifts 90 degrees to the right

• Shifts 45 degrees to the left