Sine Function Concepts and Applications

The video tutorial explains how to determine the equation of a sine function graph. It covers identifying key characteristics such as midline, amplitude, period, and phase shift. The tutorial demonstrates how to calculate these values and formulate the sine equation. Additionally, it explores finding an alternative equation using reflection across the midline.

What is the general form of the equation for a sine function graph?

• y = a * cot(bx + c) + d

• y = a * tan(bx + c) + d

• y = a * sin(bx + c) + d

• y = a * cos(bx + c) + d

What is the midline of the given sine function graph?

• y = 2

• y = 0

• y = -1

• y = 1

How is the amplitude of a sine function determined?

• Distance from the origin to a minimum

• Distance from the origin to a maximum

• Distance from the midline to the x-axis

• Distance from the midline to a maximum or minimum

What is the value of 'a' if the amplitude is 3?

• a = -3

• a = 0

• a = 3

• a = 1

How do you calculate the period of a sine function?

• 2π divided by the vertical shift

• 2π divided by b

• 2π divided by the phase shift

• 2π divided by the amplitude

What is the period of the sine function if b = π/5?

• 20

• 10

• 15

• 5

What is the phase shift if the graph is shifted left by 4 units?

• 4

• 0

• -4

• 2

What is the value of 'c' if the phase shift is -4 and b = π/5?

• -π/5

• π/5

• -4π/5

• 4π/5

What happens to the value of 'a' when there is a reflection across the midline?

• a becomes zero

• a remains unchanged

• a becomes negative

• a becomes positive

What is the alternative value of 'c' when the phase shift is right by 1 unit?

• -π/5

• π/5

• 2π/5

• -2π/5