Sine Function Properties and Graphs

The video tutorial explains how to determine possible equations for a given graph using the sine function. It covers identifying the midline, amplitude, period, phase shift, and vertical shift. The tutorial provides step-by-step instructions to calculate the values of a, b, c, and d in the equation y = a sin(bx + c) + d. Two possible equations are derived: one with a reflection across the midline and another without. The tutorial emphasizes understanding the graph's features and applying mathematical concepts to derive accurate equations.

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

• y = a * cos(bx + c) + d

• y = a * tan(bx + c) + d

• y = a * cot(bx + c) + d

• y = a * sin(bx + c) + d

What does the value of 'd' represent in the sine function equation?

• Amplitude

• Period

• Phase Shift

• Vertical Shift

How is the amplitude of a sine function determined from the graph?

• Distance from maximum to minimum

• Distance from midline to maximum or minimum

• Distance from origin to maximum

• Distance from origin to minimum

If the period of a sine function is π/2, what is the value of b?

• π/2

• π

• 4

• 2

What is the phase shift if the graph starts along the y-axis?

• 2π

• π

• 0

• π/4

What is the value of 'c' if the phase shift is zero?

• 2π

• 0

• π

• -π

In the second possible equation, what is the phase shift if the graph is shifted right by π/4 units?

• π

• π/4

• -π

• -π/4

What is the value of 'a' in the second possible equation if there is no reflection across the midline?

• 0

• -1

• -3

• 3

What is the value of 'c' in the second possible equation if the phase shift is π/4?

• -π/4

• -π

• π

• 0

Which of the following is a correct form of the second possible equation?

• y = -3 * sin(4x - π) + 1

• y = 3 * sin(4x + π) + 1

• y = 3 * sin(4x - π) + 1

• y = -3 * sin(4x + π) + 1