Cosine Function Transformations and Properties

The video tutorial explains how to derive a cosine function equation from a given graph. It covers identifying the amplitude, period, phase shift, and vertical shift. The tutorial demonstrates how to calculate these values and formulate a possible equation. Additionally, it explores an alternative equation using reflection across the midline, providing a comprehensive understanding of cosine graph transformations.

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

• y = a * sin(bx + c) + d

• y = a * cos(bx + c) + d

• y = a * tan(bx + c) + d

• y = a * sec(bx + c) + d

If the graph is reflected across the midline, what happens to the value of 'a'?

• 'a' becomes zero

• 'a' remains unchanged

• 'a' becomes positive

• 'a' becomes negative

What is the vertical shift if the midline of the graph is y = 1?

• Vertical shift is -1

• Vertical shift is 2

• Vertical shift is 1

• Vertical shift is 0

How is the amplitude of a cosine function determined from its graph?

• Distance from the midline to a maximum or minimum

• Distance between two consecutive maxima

• Distance from the y-axis to a minimum

• Distance from the x-axis to a maximum

What is the period of a cosine function if 2π/b equals π/2?

• 2π

• 4π

• π/2

• π

If the phase shift is negative π/8, what is the value of 'c' when b = 4?

• c = -π/2

• c = π/2

• c = π/4

• c = -π/4

What is the equation of the cosine function with a = 3, b = 4, c = π/2, and d = 1?

• y = -3 * cos(4x - π/2) + 1

• y = -3 * cos(4x + π/2) + 1

• y = 3 * cos(4x - π/2) + 1

• y = 3 * cos(4x + π/2) + 1

In the alternative equation, what is the value of 'a' if there is a reflection across the midline?

• a = 1

• a = 3

• a = -3

• a = 0

What is the phase shift in the alternative equation if it shifts right by π/8 units?

• c = π/2

• c = -π/2

• c = π/8

• c = -π/8

Which of the following equations represents the alternative cosine function with reflection?

• y = -3 * cos(4x - π/2) + 1

• y = 3 * cos(4x + π/2) + 1

• y = -3 * cos(4x + π/2) + 1

• y = 3 * cos(4x - π/2) + 1