Graphing Sine Functions Concepts

The video tutorial covers the process of graphing sine and cosine functions, focusing on key elements such as amplitude, period, phase shift, and vertical transformations. The instructor explains how to calculate these elements and demonstrates the graphing process with examples, emphasizing the importance of understanding the parent function and transformations.

What is the first step in graphing a sine function?

• Find the amplitude

• Determine the phase shift

• Identify the x-intercepts

• Calculate the vertical transformation

How is the amplitude of a sine function determined?

• By the period divided by four

• By the absolute value of the coefficient of the sine function

• By the coefficient of x

• By the phase shift

What is the formula for calculating the period of a sine function?

• 2π divided by the coefficient of x

• π times the coefficient of x

• 2π times the coefficient of the sine function

• π divided by the coefficient of the sine function

How does the phase shift affect the graph of a sine function?

• It modifies the vertical transformation

• It shifts the graph horizontally

• It changes the amplitude

• It alters the period

What should you do if there is no 'B' in the phase shift formula?

• Assume the phase shift is zero

• Use the coefficient of the sine function

• Set the phase shift to π/4

• Use the phase shift as given

What is the role of vertical transformations in graphing sine functions?

• They affect the phase shift

• They shift the graph up or down

• They modify the amplitude

• They change the period

How many periods should be included when graphing a sine function?

• Any of the above

• Two positive periods

• One positive period

• One positive and one negative period

What is the significance of the x-scale in graphing sine functions?

• It determines the amplitude

• It sets the distance between important points

• It defines the phase shift

• It alters the vertical transformation

What is the first step in graphing the parent function of sine?

• Identify the maximum and minimum points

• Calculate the period

• Start at the origin

• Determine the phase shift

How does the graph of a sine function repeat?

• Every π

• Every 6π

• Every 2π

• Every 4π