Understanding Sine Wave Transformations

The video tutorial explains how to derive the equation of a sine wave that is transformed by shifting the basic sine function right by two units, down by five units, and vertically stretching it by a factor of three. The process involves understanding the changes in amplitude, period, and phase shift, and how these affect the sine function's equation. The final equation is derived in the form y = a sin(b(x - d)) + c, where each parameter is adjusted according to the transformations applied.

What is the initial problem we are trying to solve in this tutorial?

• Determining the frequency of a sine wave.

• Finding the equation of a cosine wave.

• Calculating the area under a sine curve.

• Finding the equation of a sine wave after transformations.

What is the new midline of the sine function after it is shifted down?

• y = -2

• y = 5

• y = 0

• y = -5

Where does the graph of the sine function start after a horizontal shift?

• x = 2

• x = 1

• x = 0

• x = 3

How does the vertical stretching affect the amplitude of the sine function?

• It becomes 1.

• It becomes 5.

• It becomes 3.

• It remains the same.

What is the value of 'a' in the equation y = a sin(b(x - d)) + c?

• 1

• 3

• 2

• 4

What does the parameter 'b' represent in the sine function equation?

• Phase shift

• Vertical shift

• Amplitude

• Period

What is the horizontal shift 'd' in the equation of the sine function?

• 2

• 3

• 1

• 0

What is the vertical shift 'c' in the equation of the sine function?

• 0

• -5

• 5

• -2

What is the final equation of the transformed sine function?

• y = sin(x)

• y = 3 sin(x - 2) - 5

• y = 2 sin(x + 2) + 5

• y = 3 sin(x + 2) + 5

What transformations are applied to the basic sine function in this tutorial?

• Left shift, up shift, and horizontal compression

• Right shift, down shift, and vertical stretch

• Right shift, up shift, and vertical compression

• Left shift, down shift, and horizontal stretch