Graphing Sine Functions and Their Properties

The video tutorial explains how to graph the sine function with a phase shift. It begins by determining the period of the function, followed by explaining the amplitude and phase shift. The instructor solves for the phase shift and demonstrates how to graph the function manually. Finally, the video shows how to use computer tools to graph the sine function accurately.

What is the first step in sketching the graph of a sine function?

• Draw the axes

• Calculate the period

• Determine the amplitude

• Identify the phase shift

For the function sine(3x - 1/4 pi), what is the period?

• π

• π/2

• 2π

• 2π/3

What is the amplitude of the function sine(3x - 1/4 pi)?

• 3

• 2

• 1

• 1/4

How do you determine the phase shift of a sine function?

• By drawing the graph

• By calculating the period

• By solving the equation inside the sine function

• By finding the amplitude

What is the phase shift for the function sine(3x - 1/4 pi)?

• π/6

• π/12

• π/3

• π/4

What is the purpose of drawing the axes before plotting the graph?

• To find the maximum and minimum points

• To determine the amplitude

• To mark the period and phase shift

• To calculate the phase shift

How is the period marked on the graph axes?

• By marking the period length

• By dividing the axes into equal parts

• By drawing vertical lines

• By using the amplitude

What is the first point plotted on a sine graph without phase shift?

• Zero crossing

• Phase shift point

• Minimum point

• Maximum point

What happens to the points on the graph when a phase shift is applied?

• They move to the left

• They move down

• They move up

• They move to the right

How is the phase shift applied to the graph?

• By changing the amplitude

• By moving points horizontally

• By altering the period

• By moving points vertically