Understanding the Sine Function Using 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 over one period. The tutorial emphasizes the periodic nature of the sine function, demonstrating how it repeats as the angle continues to rotate around the unit circle.

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

• The sine function value

• The cosine function value

• The tangent function value

• The secant function value

At which angle does the sine function value reach +1?

• 0 radians

• π radians

• π/2 radians

• 3π/2 radians

What is the sine function value at π radians?

• -1

• Undefined

• +1

• 0

During which interval does the sine function value decrease to -1?

• 3π/2 to 2π

• π/2 to π

• 0 to π/2

• π to 3π/2

What is the sine function value at 3π/2 radians?

• 0

• +1

• -1

• Undefined

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

• It decreases to -1

• It increases to 0

• It decreases to 0

• It remains constant

What is the significance of the y-coordinate on the unit circle?

• It represents the sine function value

• It represents the cosine function value

• It represents the secant function value

• It represents the tangent function value

What is the starting value of the sine function in one period?

• +1

• 0

• Undefined

• -1