Trigonometry Identities Quiz

The video tutorial introduces the concept of trigonometric identities, starting with a review of basic algebraic concepts such as factoring and adding fractions. It then delves into reciprocal, quotient, and Pythagorean identities, explaining their significance and derivation. The tutorial includes practice on proofs and simplification of trigonometric expressions, emphasizing the importance of algebraic skills in understanding and applying these identities. The session concludes with guidance on further practice and study.

What is the result of factoring x² - 9?

• x² + 9

• x + 3

• x - 3

• (x - 3)(x + 3)

How do you add fractions with unlike denominators?

• Add the numerators directly

• Subtract the smaller denominator from the larger one

• Find a common denominator

• Multiply the denominators

What is the pattern used for factoring the difference of cubes?

• Opposite sign, same sign, always positive

• Same sign, always positive, opposite sign

• Same sign, opposite sign, always positive

• Always positive, same sign, opposite sign

Which of the following is a reciprocal identity?

• sin(x) = 1/cos(x)

• cos(x) = 1/sin(x)

• tan(x) = 1/cot(x)

• sec(x) = 1/cos(x)

What is the Pythagorean identity for sine and cosine?

• sin(x) - cos(x) = 1

• sin²(x) + cos²(x) = 1

• sin(x) + cos(x) = 1

• sin²(x) - cos²(x) = 1

How can you express tan(x) using sine and cosine?

• tan(x) = 1 / sin(x)

• tan(x) = cos(x) / sin(x)

• tan(x) = sin(x) / cos(x)

• tan(x) = sin(x) * cos(x)

What is the result of dividing the Pythagorean identity by sin²(x)?

• 1 - cot²(x) = csc²(x)

• 1 + tan²(x) = sec²(x)

• 1 + cot²(x) = csc²(x)

• 1 - tan²(x) = sec²(x)

In a trigonometric proof, what is the main rule to follow?

• Only work with one side at a time

• Work with both sides simultaneously

• Always start with the right side

• Use only sine and cosine

What is the simplified form of 1/cos(x)?

• cot(x)

• sec(x)

• tan(x)

• sin(x)

How do you simplify a complex fraction?

• Multiply the numerator by the denominator

• Use the keep-change-flip method

• Add the fractions directly

• Subtract the smaller fraction from the larger one