Understanding Sine and Cosine Functions

The video tutorial explains how to find a function in the form of y = a sin(kx) or y = a cos(kx) that matches a given graph. It identifies the pattern of the graph as resembling a sine function, thus choosing it over cosine to avoid phase shifts. The tutorial details the process of formulating the equation without phase or vertical shifts, determining the amplitude from the graph, calculating the period, and solving for k. The final equation is y = 4 sin(pi/7 x).

What is the pattern of the sine function as described in the video?

• Maximum, midline, minimum, midline

• Midline, minimum, midline, maximum

• Midline, maximum, midline, minimum

• Minimum, midline, maximum, midline

Why is the sine function preferred over the cosine function in this scenario?

• Because the cosine function is not periodic

• Because the sine function is easier to calculate

• Because the cosine function has a phase shift

• Because the sine function has a phase shift

What is the value of 'd' in the transformation of the sine function when there is no phase shift?

• d = 1

• d = 2

• d = -1

• d = 0

What does the absence of a vertical shift imply about the midline of the sine function?

• The midline is y = 2

• The midline is y = 0

• The midline is y = -1

• The midline is y = 1

What is the amplitude of the sine function as determined from the graph?

• 2 units

• 5 units

• 3 units

• 4 units

How is the amplitude of a sine function defined?

• The distance from the origin to the maximum

• The distance from the maximum to the minimum

• The distance from the midline to the maximum or minimum

• The distance from the origin to the minimum

What is the period of the sine function as calculated in the video?

• 28 units

• 21 units

• 14 units

• 7 units

How is the period of a sine function determined?

• By measuring the distance from one midline crossing to the next

• By measuring the distance from the origin to the maximum

• By measuring the distance from one maximum to the next

• By measuring the distance from the midline to the maximum

What is the value of 'k' in the final equation of the sine function?

• k = 7π

• k = π/7

• k = 2π/7

• k = π/14

What is the final equation of the sine function as derived in the video?

• y = 4 cos(7π x)

• y = 4 cos(π/7 x)

• y = 4 sin(π/7 x)

• y = 4 sin(7π x)