Basic Trigonometry Identities

The video tutorial covers the basics of trigonometric ratios and identities, explaining the difference between equations and identities. It highlights the applications of trigonometric identities in fields like engineering and architecture. The tutorial provides examples of simplifying expressions using these identities and derives the Pythagorean identities using the Pythagorean theorem.

What is the main difference between an equation and an identity?

• An equation is true for all values of the variable, while an identity is true for specific values.

• An identity is only used in algebra, not in trigonometry.

• An equation is true for specific values of the variable, while an identity is true for all values.

• An equation and an identity are the same.

In which fields are trigonometric identities commonly used?

• History and Geography

• Literature and Arts

• Civil and Mechanical Engineering

• Biology and Chemistry

How can trigonometric identities help in simplifying expressions?

• By reducing the expression to a simpler form

• By eliminating the need for calculations

• By increasing the complexity of the expression

• By changing the variables in the expression

What is the complementary angle identity for cos(90° - θ)?

• cot(θ)

• cos(θ)

• tan(θ)

• sin(θ)

Which theorem is used to derive the Pythagorean identities?

• Pythagorean Theorem

• Fermat's Last Theorem

• Binomial Theorem

• Euclidean Theorem

What is the Pythagorean identity for sin²(θ) + cos²(θ)?

• 0

• 2

• 1

• θ

How can the other two Pythagorean identities be derived from sin²(θ) + cos²(θ) = 1?

• By subtracting sin²(θ) and cos²(θ)

• By dividing by sin²(θ) and cos²(θ)

• By multiplying by sin²(θ) and cos²(θ)

• By adding sin²(θ) and cos²(θ)