Unit Circle and Triangle Relationships

Tammy explains the unit circle, focusing on finding coordinates using special right triangles. She covers the 30-60-90 and 45-45-90 triangles, detailing how to calculate coordinates for each angle in different quadrants. The video emphasizes understanding the relationships between angles and coordinates on the unit circle.

What is the radius of the unit circle?

• 3

• 2

• 1

• 0.5

Which point on the unit circle corresponds to the coordinates (1, 0)?

• Bottom

• Right

• Left

• Top

What is the coordinate of the point at the top of the unit circle?

• (0, 1)

• (1, 0)

• (0, -1)

• (-1, 0)

Which angle is associated with the first point off of zero on the unit circle?

• 45 degrees

• 60 degrees

• 30 degrees

• 90 degrees

In a 30-degree triangle, what is the ratio of the hypotenuse to the shortest side?

• 3:1

• 1:2

• 2:1

• 1:1

What is the x-coordinate of the point associated with a 30-degree angle on the unit circle?

• √3/2

• 1/2

• √2/2

• 1

For a 30-degree angle in the second quadrant, what is the sign of the x-coordinate?

• Zero

• Undefined

• Negative

• Positive

What is the angle in the third quadrant that corresponds to a 30-degree reference angle?

• 90 degrees

• 210 degrees

• 150 degrees

• 330 degrees

In a 45-45-90 triangle, what is the relationship between the legs?

• One is half the other

• They are equal

• One is double the other

• They are unrelated

What is the x-coordinate for a 45-degree angle on the unit circle?

• √3/2

• 1/2

• 1

• √2/2