Graphing Sine and Cosine Functions: Transformations and Phase Shifts

This video tutorial covers how to graph sine and cosine functions, focusing on horizontal phase shifts, amplitude, and period. It begins with basic graphing of y = sin(x) and y = cos(x), then explores variations like negative sine and cosine, vertical and horizontal stretches, and shifts. The video provides examples and practice problems, explaining how to calculate periods and apply shifts. It concludes with a discussion on domain and range, emphasizing the continuous nature of sine and cosine graphs.

What is the period of a basic sine function?

• 0

• pi

• 2pi

• 1

How does a negative value in front of sine or cosine affect its graph?

• It shifts the graph to the right

• It shifts the graph upwards

• It increases the amplitude

• It flips the graph vertically

What happens to the sine graph when the amplitude is doubled?

• The period doubles

• The graph compresses vertically

• The graph stretches vertically

• The period is halved

How do you calculate the period of a sine or cosine function with a coefficient in front of x?

• pi divided by the coefficient

• pi multiplied by the coefficient

• 2pi multiplied by the coefficient

• 2pi divided by the coefficient

What is the period of a graph of y = sin(2x)?

• 1/2pi

• 4pi

• 2pi

• pi

What is the effect of a horizontal shift on the graph of a sine function?

• No effect

• Shifts the graph left or right

• Stretches the graph horizontally

• Changes the amplitude

What is the amplitude of the graph y = 3cos(x)?

• -3

• 1

• 3

• 0

What does a vertical shift in the sine or cosine graph represent?

• Change in period

• Shift along the x-axis

• Change in amplitude

• Shift along the y-axis

How does the graph of y = sin(x) + D differ from y = sin(x)?

• It is flipped vertically

• It has a different period

• It is stretched horizontally

• It is shifted vertically

What is the effect of adding a constant inside the sine function, such as sin(x + C)?

• Change in period

• Horizontal shift

• Vertical shift

• Change in amplitude