Transformations of Trigonometric Functions

This video tutorial explores the graphs of basic trigonometric functions: sine, cosine, and tangent. It explains how to translate these graphs horizontally and vertically by manipulating their equations. The tutorial provides examples of graphing translations for each function and offers a simple method for sketching these graphs. The video concludes with a summary and encouragement for further learning.

What is the primary focus of translating trigonometric functions?

• Shifting the graph horizontally or vertically

• Changing the amplitude of the function

• Altering the frequency of the function

• Modifying the phase shift

How do you determine the direction of a horizontal translation?

• By the magnitude of the constant added to the output

• By the sign of the constant added to the input

• By the sign of the constant added to the output

• By the magnitude of the constant added to the input

What happens to a function when a positive constant is added to its output?

• The graph shifts to the right

• The graph shifts downwards

• The graph shifts upwards

• The graph shifts to the left

Which of the following is an example of a vertical translation?

• y = sin(x + π/4)

• y = cos(x - 2π/3)

• y = tan(x) + 6

• y = sin(x) - π/2

What is the effect of adding π/4 to the input of a cosine function?

• The graph shifts π/4 units downwards

• The graph shifts π/4 units upwards

• The graph shifts π/4 units to the left

• The graph shifts π/4 units to the right

In a sine function, what does adding a constant to the output do?

• It changes the amplitude

• It shifts the graph vertically

• It alters the frequency

• It modifies the phase shift

How does a tangent function differ in its range compared to sine and cosine?

• It ranges from negative to positive infinity

• It ranges from 0 to 2π

• It ranges from -1 to 1

• It has a limited range