Unit Circle and Angle Coordinates

Tammy introduces the unit circle, explaining its key points and how to find coordinates using special right triangles. She covers 30-degree, 45-degree, and 60-degree angles, detailing how to calculate coordinates using triangle properties and rationalizing denominators. The video emphasizes understanding the unit circle's geometry and applying trigonometric principles to find coordinates in different quadrants.

What is the radius of the unit circle?

• 2

• 3

• 1

• 0.5

Which point on the unit circle corresponds to the angle of 30 degrees?

• (1, 0)

• (0, 1)

• (√3/2, 1/2)

• (-1, 0)

In the second quadrant, what happens to the x-coordinate of a point associated with a 30-degree angle?

• It doubles

• It becomes negative

• It becomes positive

• It remains the same

What is the relationship between the hypotenuse and the sides in a 45-45-90 triangle?

• Hypotenuse is equal to one side

• Hypotenuse is √2 times one side

• Hypotenuse is twice one side

• Hypotenuse is half of one side

How do you rationalize the denominator of 1/√2?

• Multiply by √3/√3

• Multiply by √2/√2

• Multiply by 2/2

• Multiply by 1/√2

What are the coordinates of the point at a 45-degree angle on the unit circle?

• (-1, 0)

• (0, 1)

• (1, 0)

• (√2/2, √2/2)

For a 60-degree angle, what is the x-coordinate on the unit circle?

• 1/2

• √3/2

• 1

• 0

In the third quadrant, what happens to the coordinates of a point associated with a 60-degree angle?

• Both coordinates are negative

• X is positive, Y is negative

• X is negative, Y is positive

• Both coordinates are positive

What is the y-coordinate of the point at a 60-degree angle in the first quadrant?

• √3/2

• 1/2

• 0

• 1

Which quadrant has both coordinates negative for a 45-degree angle?

• First

• Second

• Third

• Fourth