Unit Circle and Triangle Properties

This video tutorial explains how to determine the coordinates of points on a unit circle at specific angles: 30, 45, and 60 degrees. It begins with an introduction to the unit circle and its basic coordinates. The video then demonstrates how to use the properties of right triangles and the Pythagorean theorem to find the coordinates for each angle. The process involves understanding the relationships between the sides of the triangles and rationalizing square roots to express the coordinates in a simplified form.

What is the radius of a unit circle?

• 3

• 2

• 1

• 0

Which of the following is a coordinate on the unit circle?

• (0, 3)

• (1, 0)

• (2, 0)

• (0, 2)

What are the standard angles used to identify coordinates on the unit circle?

• 60, 90, 120 degrees

• 15, 30, 45 degrees

• 30, 45, 60 degrees

• 45, 60, 90 degrees

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 1?

• 2

• 1

• 1/2

• √3/2

What is the x-coordinate for a 30-degree angle on the unit circle?

• 1/2

• √3/2

• 1

• 0

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

• 0

• 1

• √3/2

• 1/2

What is the x-coordinate for a 60-degree angle on the unit circle?

• 1/2

• √3/2

• 0

• 1

In an isosceles right triangle, what is the relationship between the lengths of the two equal sides?

• x = y

• x = 2y

• x = y/2

• x = y^2

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

• 1/2

• √3/2

• 1

• √2/2

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

• 1

• 1/2

• √3/2

• √2/2