Graphing the Sine Function

The video tutorial explains how to graph the sine function using a unit circle. It begins by setting up the x and y axes with radians and labels, then highlights key points on the sine curve. The instructor demonstrates plotting sine values from the unit circle and completes one full period of the sine curve. Intermediate points are evaluated and plotted to show the complete sine function. The video concludes with a summary of graphing sine and cosine periods.

What is the first step in graphing the sine function?

• Label the y-axis

• Draw a unit circle

• Highlight key points

• Plot the sine curve

Which of the following is a key point on the sine curve?

• Sine of 2π is 1

• Sine of π/2 is 0

• Sine of π is 0

• Sine of 3π/2 is 1

What is the sine value at π/2?

• -1

• 0.5

• 0

• 1

At which angle does the sine function return to zero after π?

• π/2

• 3π/2

• π/4

• 2π

What is the sine value at 3π/2?

• 0.5

• 0

• 1

• -1

What is the decimal approximation of sine at π/4?

• 1

• 0.866

• 0.707

• 0.5

How many main points are needed to graph one period of the sine function?

• 5

• 6

• 4

• 3

What is the period of the sine function?

• π

• 4π

• 2π

• 3π

What is the significance of the unit circle in graphing the sine function?

• It provides the y-values for sine

• It sets the period length

• It determines the amplitude

• It helps label the x-axis

What is the y-coordinate of the sine function at 0 radians?

• 0

• 0.5

• -1

• 1