Trigonometric Functions and Angles

This video tutorial covers the trigonometric function values of common angles using reference angles and triangles. It explains the side relationships in 30-60-90 and 45-45-90 triangles, and demonstrates how to calculate the six trigonometric functions for angles like 120, 210, -45, and 270 degrees. The video emphasizes the use of reference triangles and the unit circle to find exact trigonometric values without a calculator.

What is the relationship among the sides of a 30-60-90 triangle?

• 1:1:√2

• 1:2:√3

• 1:√3:2

• 1:2:2

In a 45-45-90 triangle, what is the length of the hypotenuse if each leg is 1?

• √3

• 1

• √2

• 2

How is a reference angle formed?

• By the initial side and the terminal side

• By the terminal side and the y-axis

• By the terminal side and the closest part of the x-axis

• By the initial side and the y-axis

What is the sine of a 120-degree angle?

• -√3/2

• -1/2

• √3/2

• 1/2

What is the cosine of a 120-degree angle?

• -√3/2

• √3/2

• -1/2

• 1/2

For a 210-degree angle, what is the value of the tangent?

• -1/√3

• 1/√3

• -√3

• √3

What is the sine of a negative 45-degree angle?

• √2/2

• -√2/2

• 1/√2

• -1/√2

What is the cosine of a negative 45-degree angle?

• -√2/2

• 1/√2

• √2/2

• -1/√2

What is the sine of a 270-degree angle?

• 1

• Undefined

• 0

• -1

What is the tangent of a 270-degree angle?

• 0

• Undefined

• -1

• 1