Unit Circle and Triangle Properties

This video tutorial covers the unit circle, focusing on determining x and y coordinates using special right triangles and patterns. It explains the significance of the unit circle in trigonometry, particularly in calculating sine, cosine, and tangent values. The tutorial also highlights the importance of recognizing patterns and memorizing key coordinates and angles to simplify trigonometric calculations.

What is the radius of the unit circle?

• 3

• 2

• 1

• 0

What are the coordinates of the point at 180 degrees on the unit circle?

• (0, -1)

• (-1, 0)

• (1, 0)

• (0, 1)

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

• √3/2

• √2/2

• 1

• 1/2

What is the length of the side opposite the 60-degree angle in a 30-60-90 triangle with a hypotenuse of 1?

• √2/2

• √3/2

• 1/2

• 1

What are the coordinates of the point at 30 degrees on the unit circle?

• (0, 1)

• (1, 0)

• (1/2, √3/2)

• (√3/2, 1/2)

What are the coordinates of the point at 150 degrees on the unit circle?

• (1/2, √3/2)

• (-1/2, √3/2)

• (√3/2, 1/2)

• (-√3/2, 1/2)

In a 45-45-90 triangle, what is the length of each leg if the hypotenuse is 1?

• 1

• 1/2

• √3/2

• √2/2

What are the coordinates of the point at 45 degrees on the unit circle?

• (√3/2, 1/2)

• (1, 0)

• (1/2, √3/2)

• (√2/2, √2/2)

What is the sine of 30 degrees?

• √2/2

• √3/2

• 1/2

• 1

What is the cosine of 60 degrees?

• 1

• 1/2

• √3/2

• √2/2