Sine and Cosine Graphs

What is the minimum value of the function y=cos(x)?

• 0

• -0.5

• -1

• 1

How does a phase shift affect the graph of a sine or cosine function?

• A phase shift moves the graph left or right along the x-axis, altering the starting point of the wave.

• A phase shift changes the amplitude of the wave, making it taller or shorter.

• A phase shift reflects the graph across the x-axis, inverting the wave.

• A phase shift compresses or stretches the graph vertically, changing its shape.

What is the amplitude of a sine or cosine function?

• The amplitude is the maximum distance from the center line (midline) to the peak (or trough) of the wave.

• The amplitude is the total length of one complete cycle of the wave.

• The amplitude is the frequency of the wave measured in hertz.

• The amplitude is the vertical shift of the wave from the x-axis.

What is the maximum value of the function y=sin(x)?

• 0

• 1

• 2

• -1

What is the period of a sine or cosine function?

• π

• 2π

• 3π

• 4π

What is the effect of increasing the coefficient of x in y=sin(bx)?

• It results in a longer period, meaning the function completes fewer cycles in the same interval.

• It has no effect on the function's period.

• Increasing 'b' results in a shorter period, meaning the function completes more cycles in the same interval.

• It shifts the graph vertically without affecting the period.

What is the formula for the period of a sine or cosine function with a coefficient 'b'?

• 2π/b

• π/b

• 2πb

• b/2π

What is the range of the function y=cos(x)?

• [-1, 1]

• [0, 1]

• [-2, 2]

• [1, 2]

What is a vertical shift in the context of sine and cosine graphs?

• A vertical shift moves the entire graph up or down, changing the midline of the function.

• A vertical shift only affects the amplitude of the graph.

• A vertical shift alters the frequency of the sine and cosine functions.

• A vertical shift reflects the graph across the x-axis.

What does the term 'midline' refer to in sine and cosine graphs?

• The midline is the horizontal line that runs through the center of the wave, representing the average value of the function.

• The midline is the vertical line that indicates the maximum value of the wave.

• The midline is the line that connects the peaks of the sine and cosine waves.

• The midline is the line that represents the amplitude of the wave.