Unit Circle Concepts and Definitions

The video tutorial introduces the unit circle, a circle with a radius of one unit centered at the origin of a Cartesian plane. It explains the concept of quadrants and how right angle triangles can be formed within the unit circle. The tutorial redefines sine and cosine as the y and x coordinates of a point on the unit circle, respectively. It further explores how these coordinates change with different angles, providing a new perspective on trigonometric functions.

What is the radius of the unit circle?

• 0.5 units

• 1 unit

• 3 units

• 2 units

In which quadrant are both x and y values positive?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

What is the hypotenuse of the right-angle triangle formed in the unit circle?

• x

• theta

• y

• 1

How is sine theta defined in the context of the unit circle?

• Hypotenuse

• Adjacent side

• y-coordinate

• x-coordinate

What are the coordinates of the point on the unit circle when theta is 0 degrees?

• (0, 0)

• (1, 0)

• (1, 1)

• (0, 1)

What are the coordinates of the point on the unit circle when theta is 90 degrees?

• (0, 0)

• (1, 1)

• (1, 0)

• (0, 1)

What is the new definition of sine in terms of the unit circle?

• Angle

• Radius

• y-coordinate

• x-coordinate

What is the new definition of cosine in terms of the unit circle?

• Angle

• Radius

• y-coordinate

• x-coordinate

From which axis is the angle theta measured in the unit circle?

• Positive y-axis

• Negative y-axis

• Negative x-axis

• Positive x-axis

How are sine and cosine linked in the context of the unit circle?

• Both are x-coordinates

• Both are y-coordinates

• Sine is x-coordinate, cosine is y-coordinate

• Sine is y-coordinate, cosine is x-coordinate