Simplifying Trigonometric Expressions

The video tutorial explains how to simplify trigonometric expressions by applying algebraic properties, reciprocal properties, and trigonometric identities. It covers the use of factoring and Pythagorean identities to transform complex expressions into simpler forms. The tutorial emphasizes the importance of trying different approaches and using identities to achieve simplification. Practical examples are provided to illustrate these concepts.

What is the primary goal when simplifying trigonometric expressions?

• To convert them into algebraic expressions

• To express them in their simplest form

• To make them more complex

• To eliminate all trigonometric functions

Which property allows you to rewrite x/y * 1/x as 1/y?

• Reciprocal Property

• Associative Property

• Commutative Property

• Distributive Property

What is the result of multiplying x/y by 1/z using the reciprocal property?

• y/(x*z)

• x/z

• x/(y*z)

• y/z

Which method is NOT mentioned as a factoring technique?

• Quadratic formula

• Trinomial factoring

• Difference of squares

• AC method

What is the purpose of using trigonometric identities in simplification?

• To complicate the expression

• To substitute and simplify

• To eliminate all variables

• To convert to exponential form

Which identity is used to simplify tan(θ) * cos(θ)?

• Cofunction identity

• Pythagorean identity

• Quotient identity

• Reciprocal identity

When encountering squared trigonometric terms, which identity is often applied?

• Pythagorean identity

• Quotient identity

• Cofunction identity

• Reciprocal identity

What is the Pythagorean identity for sine and cosine?

• sin(θ) / cos(θ) = 1

• sin(θ) * cos(θ) = 1

• sin²(θ) - cos²(θ) = 1

• sin²(θ) + cos²(θ) = 1

What should you do if an initial simplification attempt doesn't work?

• Multiply by zero

• Add more terms

• Try a different identity

• Give up

What is necessary when adding fractions like 1/2 + 1/3?

• Subtract the numerators

• Find a common denominator

• Multiply the denominators

• Divide the fractions