Understanding Sine and Cosine Functions

The video tutorial covers graphing trigonometric functions, focusing on sine and cosine. It explains how to graph these functions, including their negative counterparts, and discusses the concepts of amplitude, period, vertical shifts, and phase shifts. The tutorial provides step-by-step instructions for plotting these graphs and understanding the effects of changing parameters on the graph's shape.

What happens to the sine wave when a negative sign is placed in front of the function?

• It becomes a straight line.

• It flips over the x-axis.

• It shifts to the right.

• It shifts to the left.

How many key points should you plot for one cycle of a sine wave?

• Six

• Three

• Four

• Five

What is the amplitude of the function y = -3 cosine x?

• 1

• -3

• 0

• 3

If the amplitude of a sine wave is increased, what happens to the graph?

• It flips over the y-axis.

• It stretches vertically.

• It compresses horizontally.

• It shifts to the right.

How do you calculate the period of a sine function given by a sine(bx)?

• 2π divided by a

• 2π divided by b

• b divided by 2π

• a divided by 2π

What is the range of the function y = 4 cosine(πx)?

• From 0 to 4

• From -4 to 4

• From -1 to 1

• From -2 to 2

How does the graph of y = sine(2x) compare to y = sine(x)?

• It has a longer period.

• It has a shorter period.

• It has a smaller amplitude.

• It has a larger amplitude.

What effect does a vertical shift have on the graph of a sine function?

• It changes the period.

• It changes the amplitude.

• It flips the graph over the x-axis.

• It moves the graph up or down.

What is the effect of a phase shift on a sine wave?

• It flips the graph over the x-axis.

• It changes the period.

• It changes the amplitude.

• It shifts the graph left or right.

What is the phase shift of the function y = sine(x - π/2)?

• π to the left

• π/2 to the right

• π to the right

• π/2 to the left