Trigonometric Functions and Their Properties

This video tutorial covers the translations of sine and cosine graphs, focusing on phase shifts, vertical shifts, and reflections. It explains how these transformations affect the graph's position on the x-axis and y-axis. The tutorial provides examples of graphing sine and cosine functions with these shifts, helping students understand the impact of each transformation on the graph's appearance.

What is the term used for a horizontal shift in the graph of sine and cosine functions?

• Amplitude change

• Period change

• Phase shift

• Vertical shift

In the equation y = a sin(bx - d), what does the 'd' represent?

• Amplitude

• Phase shift

• Period

• Vertical shift

How does a negative phase shift affect the starting point of a sine graph?

• Increases amplitude

• Shifts it to the right

• Shifts it to the left

• Decreases amplitude

What is the amplitude of the function y = 3 cos(x + π/4)?

• 3

• 2

• 4

• 1

What effect does a vertical shift have on a graph?

• Changes its period

• Moves it left or right

• Changes its amplitude

• Moves it up or down

How is the new period of a function determined when the period is changed?

• Multiply by b

• Divide by b

• Add b

• Subtract b

What is the phase shift of the function y = sin(x + π)?

• π to the left

• π to the right

• No shift

• 2π to the right