Trigonometric Functions and Unit Circle

The video tutorial explores the concept of triangles and their properties, focusing on when a triangle is not a triangle. It delves into the basics of sine and cosine within the unit circle, providing methods to estimate these values using reference triangles. The behavior of sine and cosine as angles approach 90 and 0 degrees is analyzed, leading to an understanding of quadrantal angles and their significance in trigonometry.

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

• It becomes a square.

• It is no longer considered a triangle.

• It remains a triangle.

• It becomes a circle.

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 defined in the unit circle?

• As the y-coordinate.

• As the length of the hypotenuse.

• As the x-coordinate.

• As the angle in radians.

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

• 0.30

• 0.95

• 0.15

• 0.58

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

• It approaches 0.

• It approaches 1.

• It becomes negative.

• It remains constant.

What is the cosine value when theta is exactly 0 degrees?

• 1

• 0.5

• 0

• -1

At 180 degrees, what is the sine value?

• 0.5

• 0

• 1

• -1

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

• 0.5

• -1

• 0

• 1

Which of the following angles is considered a quadrantal angle?

• 60 degrees

• 45 degrees

• 30 degrees

• 90 degrees

At theta equal to π/2, what are the values of cosine and sine respectively?

• 0 and -1

• 0 and 1

• 1 and 0

• -1 and 0