Graphing the Sine Function with the Unit Circle

The video tutorial explains how to graph the sine function using the unit circle. It describes how the x and y coordinates on the unit circle represent cosine and sine values, respectively. The animation shows the sine function's behavior as the angle increases from 0 to 2π radians, highlighting the changes in sine values through one complete period. The tutorial emphasizes the periodic nature of the sine function, demonstrating how the graph repeats itself as the angle continues to rotate around the unit circle.

What does the x-coordinate of a point on the unit circle represent?

• Sine function value

• Cosine function value

• Cotangent function value

• Tangent function value

At what angle does the sine function value reach its maximum?

• π radians

• 2π radians

• π/2 radians

• 3π/2 radians

What is the sine function value at π radians?

• 0

• -1

• 1

• Undefined

How does the sine function value change from π to 3π/2 radians?

• Increases from -1 to 0

• Increases from 0 to 1

• Decreases from 0 to -1

• Decreases from 1 to 0

At which of the following angles is the sine function value equal to zero?

• π/2 radians

• π radians

• 0 and 2π radians

• 3π/2 radians

What demonstrates one period of the sine function?

• From π to 2π radians

• From 0 to π radians

• From π/2 to 3π/2 radians

• From 0 to 2π radians

What is the behavior of the sine function as it continues to rotate around the unit circle?

• The graph increases indefinitely

• The graph repeats itself

• The graph decreases indefinitely

• The graph remains constant

Where do the sine function values come from?

• The y-coordinates of points on the unit circle

• The radius of the unit circle

• The x-coordinates of points on the unit circle

• The diameter of the unit circle