Fundamental Trigonometric Identities Quiz

This video tutorial covers the use of fundamental trigonometric identities to simplify expressions. It begins with an introduction to quotient, reciprocal, and Pythagorean identities. The tutorial then demonstrates how to simplify trigonometric expressions using these identities, including factoring and substitution techniques. Advanced simplification methods are explored, highlighting the possibility of multiple solutions. The video concludes with strategies for adding and subtracting trigonometric expressions, emphasizing the importance of finding a common denominator.

Which of the following is a quotient identity?

• cos(θ) = 1/sec(θ)

• tan(θ) = sin(θ)/cos(θ)

• cot(θ) = cos(θ)/sin(θ)

• sin(θ) = 1/csc(θ)

What is the reciprocal of sec(θ)?

• sin(θ)

• cos(θ)

• tan(θ)

• cot(θ)

How can you simplify sin(x) * cot(x)?

• sec(x)

• cos(x)

• tan(x)

• csc(x)

What is the simplified form of sin^2(x) + cos^2(x)?

• cos(x)

• sin(x)

• 1

• 0

Which identity can be used to simplify sec^2(θ) - 1?

• tan^2(θ)

• cot^2(θ)

• sin^2(θ)

• cos^2(θ)

What is the result of factoring cos^2(x) - sin^2(x)?

• (cos(x) - sin(x))(cos(x) - sin(x))

• (cos(x) + sin(x))(cos(x) + sin(x))

• (cos(x) - sin(x))(cos(x) + sin(x))

• (cos(x) + sin(x))(cos(x) - sin(x))

How do you simplify (cos(x) - 2) / (cos^2(x) - 4)?

• 1 / (cos(x) - 2)

• cos(x) + 2

• 1 / (cos(x) + 2)

• cos(x) - 2

What is the common denominator for adding sin(θ)/(1 + cos(θ)) and cos(θ)/sin(θ)?

• sin(θ)

• 1 + cos(θ)

• cos(θ)(1 + sin(θ))

• sin(θ)(1 + cos(θ))

What is the simplified form of 1/sin(θ)?

• sec(θ)

• csc(θ)

• cot(θ)

• tan(θ)

What is the result of simplifying 2 / (1 - cos^2(θ))?

• 2 * sec^2(θ)

• 2 * csc^2(θ)

• 2 * tan^2(θ)

• 2 * cot^2(θ)