Trigonometric Functions and Their Properties

The video tutorial covers transformations of sine and cosine functions, focusing on amplitude, period, phase shift, and vertical shift. It explains how these transformations affect the graph of the functions and provides examples of graphing transformed functions. The tutorial emphasizes understanding the key values in the equations to determine the changes in the graph.

What is the primary focus of transformations in sine and cosine functions?

• Changing the color of the graph

• Modifying the basic graph structure

• Altering the graph's thickness

• Adjusting the graph's position on the y-axis

What does the 'a' value in a trigonometric function primarily affect?

• The graph's phase shift

• The graph's period

• The graph's amplitude

• The graph's color

How does a negative 'a' value affect the graph of a trigonometric function?

• It increases the graph's amplitude

• It reflects the graph over the x-axis

• It reflects the graph over the y-axis

• It changes the graph's color

What does the 'b' value in a trigonometric function determine?

• The graph's vertical shift

• The graph's amplitude

• The graph's period

• The graph's phase shift

How do you calculate the period of a sine or cosine function using the 'b' value?

• Divide 2π by the absolute value of b

• Multiply 2π by the absolute value of b

• Subtract 2π from the absolute value of b

• Add 2π to the absolute value of b

What does the 'c' value in a trigonometric function indicate?

• The graph's phase shift

• The graph's period

• The graph's vertical shift

• The graph's amplitude

How is the phase shift of a trigonometric function calculated?

• By dividing c by b

• By subtracting c from b

• By adding c to b

• By multiplying c by b

What does the 'd' value in a trigonometric function represent?

• The graph's period

• The graph's vertical shift

• The graph's amplitude

• The graph's phase shift

In the function y = sin(5x), what is the period of the graph?

• 5π

• 2π/5

• π

• 2π

For the function y = sin(5x), what is the amplitude?

• 5

• 1

• 0.5

• 10