Trigonometric Functions and Special Triangles

This video tutorial explains how to evaluate an expression involving sine and cosine using special triangles and radian measures. It covers the properties of 45-45-90 and 30-60-90 triangles, and demonstrates how to calculate sine and cosine for angles like π/4 and π/6. The tutorial also includes steps for simplifying trigonometric expressions through arithmetic operations, ensuring a comprehensive understanding of the problem-solving process.

Which angles are involved in the expression to be evaluated?

• Pi/3 and Pi/4

• Pi/4 and Pi/6

• Pi/6 and Pi/2

• Pi/3 and Pi/6

What is the main focus of the video tutorial?

• Exploring the unit circle

• Understanding the Pythagorean theorem

• Learning about the history of trigonometry

• Evaluating an expression using special triangles and radian measure

What are the angles in a 45-45-90 triangle?

• 30, 30, 120

• 60, 60, 60

• 45, 45, 90

• 30, 60, 90

What is the sine of 45 degrees in a 45-45-90 triangle?

• √2/2

• 1/2

• √3/2

• 1

What is the cosine of 45 degrees in a 45-45-90 triangle?

• 1

• √2/2

• √3/2

• 1/2

What is the sine of 30 degrees in a 30-60-90 triangle?

• √2/2

• 1/2

• 1

• √3/2

What is the cosine of 30 degrees in a 30-60-90 triangle?

• √3/2

• √2/2

• 1/2

• 1

What is the first step in simplifying the expression?

• Add the fractions

• Divide the fractions

• Subtract the fractions

• Multiply the fractions

What is the result of multiplying √2 and √3?

• √6

• √8

• √9

• √5

What is the final simplified form of the expression?

• 2 + √3/4

• 1 - √3/4

• 1 + √3/4

• 2 - √3/4