Exploring Sine and Cosine Function Values

This video tutorial covers the sine and cosine functions, focusing on the 45-45-90 and 30-60-90 special right triangles. It explains how to use radians instead of degrees and how to label a unit circle with these angles. The tutorial emphasizes the importance of memorizing key values and provides tips for doing so. It also includes exercises to practice identifying sine and cosine values on the unit circle.

What is the hypotenuse length of a 45-45-90 triangle if the legs are of length 1?

• 2

• sqrt(2)

• 1.5

• 1

What is the sine of pi/4?

• 1/2

• sqrt(2)/2

• sqrt(3)/2

• 1

What coordinates represent the point for pi/4 on the unit circle?

• (-sqrt(2)/2, sqrt(2)/2)

• (sqrt(2)/2, sqrt(2)/2)

• (0, 1)

• (1, 0)

What is the cosine of 3 pi/4?

• 0

• sqrt(2)/2

• -sqrt(2)/2

• 1

Which coordinate pair represents the cosine and sine of pi/2 on the unit circle?

• (-1, 0)

• (0, -1)

• (1, 0)

• (0, 1)

What is the cosine of pi/6 in a 30-60-90 triangle?

• sqrt(3)/2

• 1/2

• 2

• sqrt(2)/2

In a 30-60-90 triangle, what is the length across from the 30-degree angle?

• 2

• sqrt(2)

• 1

• sqrt(3)

What is the sine of pi/3 in a 30-60-90 triangle?

• sqrt(3)/2

• sqrt(2)/2

• 2

• 1/2

How is the cosine of pi/6 calculated in a 30-60-90 triangle?

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Adjacent over opposite

• Opposite over hypotenuse

Which of the following is a method to simplify memorization of the unit circle?

• Using a calculator for each point

• Memorizing all angles in degrees

• Identifying patterns and symmetries

• Drawing the circle repeatedly