Understanding Cosine and Sine Functions on the Unit Circle

This lesson uses Desmos animation to connect cosine and sine values on the unit circle with their graphs on the coordinate plane. It explains the unit circle's key points and demonstrates graphing one period of the cosine and sine functions. The video also animates these functions together, showing their relationship as the point moves around the unit circle.

What is the relationship between the x-coordinate on the unit circle and the cosine function?

• The x-coordinate is equal to the secant function.

• The x-coordinate is equal to the sine function.

• The x-coordinate is equal to the cosine function.

• The x-coordinate is equal to the tangent function.

At which angle is the cosine function value equal to zero?

• 2π radians

• π radians

• 0 radians

• π/2 radians

What is the cosine function value at π radians?

• 1

• 0

• 2

• -1

How does the x-coordinate change from π to 3π/2 radians on the unit circle?

• Decreases from 1 to 0

• Increases from -1 to 0

• Decreases from 0 to -1

• Increases from 0 to 1

What is the pattern for one period of the basic cosine function?

• Max, midline, min, midline, max

• Midline, max, midline, min, midline

• Min, midline, max, midline, min

• Max, min, max, min, max

At which angle is the sine function value equal to one?

• 3π/2 radians

• π/2 radians

• 0 radians

• π radians

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

• 0

• 1

• -1

• 2

How does the y-coordinate change from 0 to π/2 radians on the unit circle?

• Increases from 0 to 1

• Decreases from 1 to 0

• Decreases from 0 to -1

• Increases from -1 to 0

What is the pattern for one period of the basic sine function?

• Max, min, max, min, max

• Max, midline, min, midline, max

• Midline, max, midline, min, midline

• Min, midline, max, midline, min

What color represents the sine function in the animation?

• Blue

• Purple

• Red

• Green