Trigonometric Identities and Simplifications

This video tutorial introduces trigonometric identities, focusing on their definitions and applications in evaluating functions, simplifying expressions, and solving equations. It covers the eight fundamental identities, including quotient, reciprocal, and Pythagorean identities. The tutorial demonstrates how to find exact values of trigonometric functions using these identities and provides techniques for simplifying expressions. Advanced methods for handling complex expressions are also discussed, making the content suitable for those interested in deepening their understanding of trigonometry.

Which of the following is a quotient identity?

• tan(θ) = sin(θ) / cos(θ)

• sec(θ) = 1 / cos(θ)

• sin(θ) = 1 / csc(θ)

• cos(θ) = 1 / sec(θ)

What is the Pythagorean identity involving sine and cosine?

• sin²(θ) - cos²(θ) = 1

• cos²(θ) + sin²(θ) = 1

• tan²(θ) + 1 = sec²(θ)

• cot²(θ) + 1 = csc²(θ)

Given cos(θ) = -4/7 and θ is in the second quadrant, what is sin(θ)?

• √33 / 7

• -√33 / 7

• -4 / 7

• 4 / 7

If cot(θ) = 2/5, what is sec(θ)?

• -√29 / 2

• 2 / √29

• √29 / 2

• -2√29 / 29

What is the simplified form of sin(θ) * sec(θ)?

• tan(θ)

• cos(θ)

• 1

• sin²(θ)

How can you rewrite tan(θ) using sine and cosine?

• 1 / cos(θ)

• 1 / sin(θ)

• cos(θ) / sin(θ)

• sin(θ) / cos(θ)

What is the result of simplifying 2 * (sec²(θ) - tan²(θ))?

• 2

• tan²(θ)

• 1

• sec²(θ)

What is the simplified form of 2 - 2sin²(θ) / cos(θ)?

• cos²(θ)

• 2cos(θ)

• 1 - sin²(θ)

• 2sin(θ)

How do you simplify sin²(θ) - cos²(θ) * sin²(θ)?

• 1 - cos²(θ)

• sin⁴(θ)

• cos⁴(θ)

• 1 - sin²(θ)

What is the simplified form of sin(θ) * cos(θ) / tan(θ)?

• cos²(θ)

• sin²(θ)

• tan²(θ)

• 1