Unit Circle Trigonometric Concepts

The video tutorial redefines sine, cosine, and tangent using the unit circle instead of triangles. It explains how to determine the coordinates of points on the unit circle and how these relate to trigonometric functions. The tutorial also covers the use of calculators to verify trigonometric values and explores special angles like 0, 90, 180, and 270 degrees. The session concludes with a summary of the key concepts discussed.

What is the new perspective on sine, cosine, and tangent introduced in the video?

• They are defined using rectangles.

• They are defined using right triangles.

• They are defined using the unit circle.

• They are defined using squares.

How is cosine defined in terms of the unit circle?

• As the diameter of the unit circle.

• As the x-coordinate of a point on the unit circle.

• As the radius of the unit circle.

• As the y-coordinate of a point on the unit circle.

What does the angle theta represent in the context of the unit circle?

• The angle between the positive y-axis and the radius.

• The angle between the positive x-axis and the radius to a point.

• The angle between two radii of the circle.

• The angle between the negative x-axis and the radius.

What are the coordinates of the point on the unit circle at 0 degrees?

• (0, -1)

• (0, 1)

• (-1, 0)

• (1, 0)

What is the sine of 90 degrees on the unit circle?

• -1

• 1

• 0

• 0.5

What is the cosine of 180 degrees on the unit circle?

• -1

• 0.5

• 0

• 1

What is the angle for the point with coordinates (0, -1) on the unit circle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

What is the cosine of 270 degrees on the unit circle?

• 0.5

• 0

• 1

• -1

What is the sine of 270 degrees on the unit circle?

• -1

• 1

• 0

• 0.5

Which of the following angles cannot exist in a triangle?

• 30 degrees

• 90 degrees

• 180 degrees

• 60 degrees