Understanding Ordered Pairs in a Unit Circle

The video tutorial introduces the concept of ordered pairs in a unit circle, focusing on 45° steps. It explains the significance of the 45° triangle and how to calculate ordered pairs for each quadrant. The tutorial concludes with a summary of the ordered pairs for 45° angles in a unit circle.

What is the primary focus of the video tutorial?

• Understanding the unit circle

• Learning about 30° steps

• Exploring ordered pairs for 45° steps

• Studying the Pythagorean theorem

What is the significance of the 45°-45°-90° triangle in the unit circle?

• It helps in calculating the radius

• It is used to find the hypotenuse

• It simplifies the calculation of ordered pairs

• It determines the angle of rotation

How do you calculate the leg of a 45°-45°-90° triangle in a unit circle?

• Multiply the hypotenuse by √2

• Divide the hypotenuse by √2

• Add the hypotenuse to √2

• Subtract √2 from the hypotenuse

What is the value of each leg in a 45°-45°-90° triangle when the hypotenuse is 1?

• 1/√2

• √2

• 1

• √2/2

In which quadrant are both x and y coordinates positive?

• Quadrant I

• Quadrant II

• Quadrant IV

• Quadrant III

What are the signs of the coordinates in Quadrant II?

• Positive x, Positive y

• Negative x, Positive y

• Negative x, Negative y

• Positive x, Negative y

Which quadrant has both coordinates negative?

• Quadrant III

• Quadrant II

• Quadrant IV

• Quadrant I

In Quadrant IV, what is the sign of the y-coordinate?

• Zero

• Undefined

• Negative

• Positive

What is the ordered pair for 135° in the unit circle?

• (-√2/2, √2/2)

• (-√2/2, -√2/2)

• (√2/2, √2/2)

• (√2/2, -√2/2)

What is the ordered pair for 225° in the unit circle?

• (√2/2, √2/2)

• (-√2/2, √2/2)

• (-√2/2, -√2/2)

• (√2/2, -√2/2)