Unit Circle Coordinates and Properties

The video tutorial explains how to find terminal points on the unit circle, focusing on exact values rather than decimal approximations. It covers basic coordinates, such as 1, 0 and -1, 0, and delves into deriving coordinates for PI over 4 and PI over 6 using the Pythagorean theorem and 30-60-90 triangles. The tutorial also includes solving example problems to reinforce the concepts.

What is the main goal when finding terminal points on the unit circle?

• To find decimal approximations of angles

• To measure the radius of the circle

• To calculate the circumference of the circle

• To determine the exact coordinates where an angle ends

What are the coordinates of the point at π on the unit circle?

• (1, 0)

• (0, 1)

• (-1, 0)

• (0, -1)

How is the unit circle typically divided to find terminal points?

• Into quarters and eighths

• Into thirds and fifths

• Into π/4 and π/6 segments

• Into π/3 and π/5 segments

What type of triangle is used to find the coordinates for π/4?

• 45-45-90 triangle

• Equilateral triangle

• Scalene triangle

• 30-60-90 triangle

What are the coordinates for π/4 on the unit circle?

• (√2/2, √2/2)

• (√3/2, 1/2)

• (0, 1)

• (1, 0)

How do the signs of the coordinates change in different quadrants for π/4?

• They remain the same in all quadrants

• Both coordinates change sign depending on the quadrant

• Only the x-coordinate changes sign

• Only the y-coordinate changes sign

What type of triangle is used to find the coordinates for π/6?

• Scalene triangle

• Equilateral triangle

• 45-45-90 triangle

• 30-60-90 triangle

What are the coordinates for π/6 on the unit circle?

• (√3/2, 1/2)

• (√2/2, √2/2)

• (0, 1)

• (1, 0)

How do the coordinates for π/6 change as you move around the unit circle?

• Only the y-coordinate changes

• Only the x-coordinate changes

• They switch places and change signs

• They remain constant

What are the coordinates of the terminal point for 7π/4?

• (√2/2, √2/2)

• (√2/2, -√2/2)

• (-√2/2, √2/2)

• (-√2/2, -√2/2)