Trigonometric Values and Concepts

The video tutorial explores the concept of triangles and their properties, focusing on when a triangle is not a triangle. It introduces the basics of sine and cosine in the unit circle, explaining how these trigonometric functions relate to the x and y coordinates. The tutorial provides methods for estimating sine and cosine values using reference triangles and examines the behavior of these functions as angles approach 90 and 0 degrees. It concludes with an analysis of sine and cosine at quadrantal angles, emphasizing their significance in trigonometry.

What happens to a triangle when one of its legs has a length of zero?

• It is no longer considered a triangle.

• It becomes a circle.

• It remains a triangle.

• It becomes a square.

In the unit circle, what does the sine of an angle represent?

• The angle in degrees.

• The y-coordinate.

• The x-coordinate.

• The length of the hypotenuse.

How is the cosine of an angle in the unit circle defined?

• As the length of the hypotenuse.

• As the angle in radians.

• As the x-coordinate.

• As the y-coordinate.

What is the estimated cosine value when theta is slightly larger than in the previous triangle?

• 0.15

• 0.58

• 0.30

• 0.95

As theta approaches 90 degrees, what happens to the sine value?

• It approaches 0.

• It remains constant.

• It becomes negative.

• It approaches 1.

What is the sine value at 0 degrees or 0 radians?

• 1

• 0

• -1

• Undefined

At 180 degrees or π radians, what is the cosine value?

• Undefined

• -1

• 0

• 1

What is the sine value at 270 degrees or 3π/2 radians?

• Undefined

• -1

• 0

• 1

Which of the following angles is considered a quadrantal angle?

• 45 degrees

• 90 degrees

• 60 degrees

• 30 degrees

What is the cosine value at π/2 radians?

• 1

• 0

• -1

• Undefined