Cosine Function Concepts and Applications

The video tutorial explains how to determine an equation for a given graph using the cosine function. It covers the process of identifying the amplitude, period, phase shift, and vertical shift to form the equation in the format y = a * cos(bx + c) + d. The tutorial also demonstrates how to calculate these values by analyzing the graph and provides two possible equations, one with and one without reflection across the midline.

What is the general form of the cosine function used to determine the equation of a graph?

• y = a * sec(bx + c) + d

• y = a * sin(bx + c) + d

• y = a * cos(bx + c) + d

• y = a * tan(bx + c) + d

What is the amplitude of a cosine function?

• The distance from the midline to a maximum or minimum point

• The horizontal distance between two consecutive maxima

• The vertical shift of the graph

• The phase shift of the graph

How do you determine the vertical shift of a cosine graph?

• By finding the distance between the maximum and minimum points

• By identifying the midline of the graph

• By measuring the horizontal shift

• By calculating the period of the graph

What is the formula to calculate the period of a cosine function?

• 2π divided by the amplitude

• 2π divided by the phase shift

• 2π divided by b

• 2π divided by the vertical shift

If the period of a cosine function is 10, what is the value of b?

• π/5

• 5π

• 10π

• π/10

How is the phase shift of a cosine graph determined?

• By calculating the horizontal shift from the y-axis

• By identifying the amplitude

• By finding the distance between two consecutive maxima

• By measuring the vertical distance from the midline

What is the phase shift if the graph is shifted left by 1.5 units?

• -3π/10

• -1.5

• 3π/10

• 1.5

What is the value of c if the phase shift is 3π/10?

• -7π/10

• 7π/10

• -3π/10

• 3π/10

What is the effect of a reflection across the midline on the value of a?

• It halves the value of a

• It doubles the value of a

• It makes a negative

• It makes a positive

Which of the following equations represents a cosine graph with a reflection across the midline?

• y = 3 * cos(π/5 * x + 3π/10)

• y = 3 * cos(π/5 * x - 7π/10)

• y = -3 * cos(π/5 * x + 3π/10)

• y = -3 * cos(π/5 * x - 7π/10)