How to Find All of the Transformations for the Graph of Sine

The video tutorial covers the concepts of amplitude, period, phase shift, and vertical translation in trigonometric functions. It begins with an introduction to amplitude and period, followed by an explanation of the sine function formula. The tutorial then demonstrates how to calculate the period and discusses the concept of phase shift, including how to determine it from the function's equation. Finally, it explains vertical translation and its effect on graphing functions.

What is the amplitude of a trigonometric function represented by the equation y = a sin(Bx - C) + D?

• The value of B

• The absolute value of a

• The value of C

• The value of D

How do you calculate the period of a sine function given by y = a sin(Bx - C) + D?

• 2π divided by B

• 2π times B

• B times 2π

• B divided by 2π

In the context of graphing trigonometric functions, what is the significance of the X scale?

• It determines the amplitude

• It affects the vertical translation

• It helps in plotting the graph accurately

• It changes the phase shift

What is the phase shift of the function y = a sin(Bx - C) + D if the equation inside the parentheses is set to zero?

• C/B

• B/C

• C

• B

If a sine function is shifted vertically by a value of D, what does this represent?

• A phase shift

• A vertical translation

• A change in period

• A change in amplitude