Understanding the Unit Circle

The video tutorial covers the unit circle, starting with a recap of its connection to special right triangles. It explains the key characteristics of the unit circle, including the coordinates at 0, 90, 180, and 270 degrees. The focus then shifts to the first quadrant, detailing the angles of 30, 45, and 60 degrees, and their corresponding cosine and sine values. The tutorial extends this knowledge to other quadrants, highlighting patterns and relationships. Finally, it provides practice problems to reinforce understanding and application of the unit circle concepts.

What is the ordered pair for 0 degrees on the unit circle?

• (0, -1)

• (1, 0)

• (0, 1)

• (-1, 0)

In which quadrant are both x and y coordinates positive?

• Third Quadrant

• Fourth Quadrant

• Second Quadrant

• First Quadrant

Which trigonometric function comes first in an ordered pair on the unit circle?

• Sine

• Cosine

• Tangent

• Secant

What is the cosine of 30 degrees?

• 0

• 1/2

• √3/2

• √2/2

What is the sine of 45 degrees?

• 1/2

• √3/2

• √2/2

• 0

How does knowing the first quadrant help in understanding the entire unit circle?

• It provides the basic angles and their coordinates.

• It shows the negative angles.

• It explains the concept of radians.

• It gives the values of tangent.

What is the cosine of 135 degrees?

• -√2/2

• √2/2

• -1/2

• 1/2

What is the sine of -300 degrees?

• √3/2

• -1/2

• -√3/2

• 1/2

What is the cosine of 210 degrees?

• -√3/2

• √3/2

• -1/2

• 1/2

Which angle corresponds to the ordered pair (-√2/2, √2/2)?

• 225 degrees

• 45 degrees

• 135 degrees

• 315 degrees