Understanding Cosine Function from a Graph

The video tutorial explains how to determine the equation of a cosine function from a graph. It covers identifying maximum and minimum values to find the midline, calculating amplitude, determining the period to find the B value, and identifying phase shift for the C value. The final equation is constructed using these values.

What is the general form of the cosine function used in this video?

• y = a sec(B(x - C)) + D

• y = a tan(B(x - C)) + D

• y = a cos(B(x - C)) + D

• y = a sin(B(x - C)) + D

How is the midline of the graph determined?

• By finding the average of the maximum and minimum y-values

• By finding the difference between the maximum and minimum y-values

• By finding the sum of the maximum and minimum y-values

• By finding the product of the maximum and minimum y-values

What is the amplitude of the cosine function in this example?

• 4

• 3

• 1

• 2

How is the amplitude of a cosine function defined?

• The distance from the midline to the minimum value

• The distance from the midline to the maximum value

• The distance from the y-axis to the maximum value

• The distance from the x-axis to the maximum value

What is the normal period of a cosine function in degrees?

• 180 degrees

• 270 degrees

• 360 degrees

• 450 degrees

How is the B value calculated in this example?

• By adding the new period to the original period

• By subtracting the new period from the original period

• By dividing the new period by the original period

• By multiplying the new period by the original period

What is the observed period of the graph in this example?

• 540 degrees

• 720 degrees

• 360 degrees

• 810 degrees

Where does the first maximum of the graph occur, indicating the phase shift?

• 0 degrees

• 180 degrees

• 45 degrees

• 90 degrees

What is the phase shift (C value) in this example?

• 180 degrees

• 90 degrees

• 0 degrees

• -90 degrees

What is the final equation of the cosine function derived in this video?

• y = 2 cos(0.5(x + 90)) - 2

• y = 2 cos(0.5(x - 90)) + 2

• y = 2 cos(0.5(x - 90)) - 2

• y = 2 cos(0.5(x + 90)) + 2