Exploring the Unit Circle in Trigonometry

The video tutorial introduces the unit circle, explaining its significance and how it is used to define trigonometric functions. It covers the basic properties of the unit circle, such as its radius and key coordinates. The tutorial then discusses angle conventions, focusing on positive angles and their representation. It extends the traditional definitions of sine, cosine, and tangent using the unit circle, allowing for the evaluation of these functions for any angle. The video concludes by setting up new definitions for trigonometric functions that are consistent with the unit circle approach.

What is the radius of a unit circle?

• -1

• 1

• 0

• 2

Which direction do you move to draw a positive angle on the unit circle?

• Counterclockwise

• Clockwise

• Straight down

• Straight up

What is the cosine of an angle in terms of the unit circle?

• The x-coordinate where it intersects

• The radius of the circle

• The y-coordinate where it intersects

• The angle itself

How is the sine of an angle defined using the unit circle?

• The angle itself

• The radius of the circle

• The x-coordinate of the intersection

• The y-coordinate of the intersection

What does tangent of an angle equal to in terms of the unit circle?

• The x-coordinate over the y-coordinate

• The radius over the x-coordinate

• The y-coordinate over the x-coordinate

• The angle itself