Sine and Cosine Graph Properties

The video tutorial covers the properties and characteristics of sine and cosine graphs, including their amplitude, period, and frequency. It explains how these graphs are bounded and how transformations can affect their appearance. The tutorial also discusses the mathematical equations used to represent these graphs and how to calculate their amplitude and period.

What is the range of the parent function for sine and cosine graphs?

• From -1 to 0

• From 0 to 1

• From -1 to 1

• From -2 to 2

Which equation represents a transformation of the sine function?

• y = a * tan(BX - C) + D

• y = a * sin(BX - C) + D

• y = a * cos(BX - C) + D

• y = a * sec(BX - C) + D

How is the amplitude of a sine or cosine graph determined?

• By the value of D

• By the absolute value of A

• By the value of C

• By the value of B

What does the amplitude of a graph represent?

• The distance from the x-axis to the max

• The half distance from max to min

• The full distance from max to min

• The distance from the y-axis to the min

How is the period of a sine or cosine function calculated?

• 2π divided by the absolute value of A

• 2π divided by the absolute value of B

• π divided by the absolute value of A

• π divided by the absolute value of B

What does the period of a graph indicate?

• The time it takes for the graph to reach its minimum

• The time it takes for the graph to complete a cycle

• The time it takes for the graph to reach its maximum

• The time it takes for the graph to cross the x-axis

How is the frequency of a sine or cosine function determined?

• Absolute value of A divided by 2π

• Absolute value of B divided by 2π

• Absolute value of C divided by 2π

• Absolute value of D divided by 2π

What does the frequency of a graph represent?

• The number of cycles in a period

• The number of maximum points in a period

• The number of minimum points in a period

• The number of x-axis crossings in a period

What happens to the graph if the value of 'a' is negative?

• The graph reflects over the x-axis

• The graph reflects over the y-axis

• The graph shifts to the left

• The graph shifts to the right

What effect does the value of 'a' have on the graph?

• It affects the frequency

• It affects the phase shift

• It affects the period

• It affects the amplitude