Understanding Ordered Pairs in a Unit Circle

The video tutorial explains how to find ordered pairs for 30 and 60-degree angles in a unit circle. It begins with an introduction to the unit circle and the concept of ordered pairs. The tutorial then delves into the analysis of 30-degree and 60-degree angles, using right triangles to determine the coordinates. Finally, it discusses how these coordinates mirror across different quadrants, providing a comprehensive understanding of ordered pairs in a unit circle.

What is the radius of the unit circle?

• 2

• 1

• 0.5

• 3

In a 30-60-90 triangle, what is the length of the short leg if the hypotenuse is 1?

• 1

• 0.5

• √2/2

• √3/2

What is the ordered pair for a 30-degree angle in the unit circle?

• (√3/2, 0.5)

• (0.5, √3/2)

• (1, 0)

• (√2/2, √2/2)

How do you calculate the long leg of a 30-60-90 triangle?

• Short leg times √3

• Hypotenuse times √3

• Hypotenuse times √2

• Short leg times √2

What is the ordered pair for a 60-degree angle in the unit circle?

• (0, 1)

• (1, 0)

• (0.5, √3/2)

• (√3/2, 0.5)

How are the coordinates in the second quadrant related to those in the first quadrant?

• They are mirror images over the x-axis

• They are mirror images over the y-axis

• They are negatives of each other

• They are the same

What happens to the coordinates when mirrored over the x-axis?

• Only x-coordinate changes sign

• Only y-coordinate changes sign

• Both coordinates become negative

• Both coordinates become positive

In which quadrant are both coordinates negative?

• Fourth

• Third

• Second

• First

What is the ordered pair for a point in the fourth quadrant?

• (-0.5, -√3/2)

• (-√3/2, 0.5)

• (√3/2, -0.5)

• (0.5, √3/2)

How are the coordinates in the fourth quadrant related to those in the first quadrant?

• They are mirror images over the x-axis

• They are negatives of each other

• They are mirror images over the y-axis

• They are the same