Trigonometric Functions and Unit Circle

This video tutorial introduces the unit circle and explains the trigonometric definitions of sine and cosine. It begins with a review of angles and the Cartesian coordinate system, then defines sine and cosine using the unit circle. The tutorial demonstrates how angles correspond to points on the unit circle and provides examples of different angles and their associated points. Finally, it defines the cosine function as the x-coordinate and the sine function as the y-coordinate of these points.

What is the primary focus of the unit circle in trigonometry?

• To calculate the area of a circle

• To find the diameter of a circle

• To understand the relationship between angles and coordinates

• To measure the circumference of a circle

What is the radius of the unit circle?

• 2

• 3

• 1

• 0.5

In the trigonometric definition, what is the input of the function?

• The diameter of the circle

• An angle

• The radius of the circle

• A point on the circle

What is the output of the trigonometric function described in the video?

• A single number

• A line segment

• An ordered pair

• A triangle

Which quadrant is associated with angles less than 90 degrees?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the point associated with an angle of 90 degrees on the unit circle?

• (0, 1)

• (1, 0)

• (0, -1)

• (-1, 0)

What is the point associated with an angle of 180 degrees?

• (-1, 0)

• (0, -1)

• (1, 0)

• (0, 1)

What is the point associated with an angle of 360 degrees?

• (1, 0)

• (0, 1)

• (-1, 0)

• (0, -1)

What is the point associated with an angle of 270 degrees?

• (0, 1)

• (0, -1)

• (1, 0)

• (-1, 0)

How is a negative angle measured on the unit circle?

• From the origin

• Clockwise from the x-axis

• Counterclockwise from the x-axis

• From the y-axis