Graphing the Cosine Function with the Unit Circle

The video tutorial explains the graph of the cosine function using the unit circle. It illustrates how the cosine function is represented as the x-coordinate of a point on the unit circle where the terminal side of an angle intersects. The video covers key angles such as 0, 90, 180, 270, and 360 degrees, showing how the cosine values change. It also discusses the domain and range of the cosine function, emphasizing that the domain is all real numbers and the range is from -1 to 1. The tutorial includes an animation to visualize these concepts.

What does the cosine function equal to on the unit circle?

• The y-coordinate of the point

• The x-coordinate of the point

• The angle in radians

• The length of the radius

What is the value of cosine at 0 degrees?

• 0

• -1

• 1

• Undefined

What is the cosine value at 90 degrees?

• -1

• Undefined

• 0

• 1

At what angle does the cosine function reach its minimum value?

• 360 degrees

• 270 degrees

• 90 degrees

• 180 degrees

What is the cosine value at 180 degrees?

• 1

• 0

• Undefined

• -1

How does the cosine function behave as it completes one revolution?

• It reaches its maximum value

• It returns to its starting value

• It becomes undefined

• It reaches its minimum value

What does the animation of the cosine function help illustrate?

• Its relation to the sine function

• Its maximum value only

• Its behavior and properties

• Its undefined points

Can the cosine function make multiple revolutions around the unit circle?

• No, only once

• No, it stops at 270 degrees

• Yes, indefinitely

• Yes, but only twice

What is the domain of the cosine function?

• Positive real numbers

• All real numbers

• -1 to 1

• 0 to 1

What is the range of the cosine function?

• All real numbers

• -1 to 1

• 0 to 1

• Positive real numbers