Trigonometric Expressions and Identities

The video tutorial explains how to simplify a trigonometric expression by converting tangent and secant functions into sine and cosine. It involves substituting these functions, handling complex fractions by multiplying with reciprocals, and using the Pythagorean identity to simplify the expression further. The process concludes with factoring and recognizing identities to achieve the final simplified result.

What is the first step in simplifying a trigonometric expression?

• Convert all terms to tangent and secant

• Convert all terms to sine and cosine

• Add all terms together

• Multiply all terms by 2

What is the equivalent of tangent x in terms of sine and cosine?

• 1 / sine x

• 1 / cosine x

• sine x / cosine x

• cosine x / sine x

What is the equivalent of secant x in terms of cosine?

• cosine x

• sine x

• 1 / sine x

• 1 / cosine x

How do you handle a complex fraction in a trigonometric expression?

• Add the fractions together

• Multiply by the reciprocal of the denominator

• Subtract the denominator from the numerator

• Divide the numerator by the denominator

What happens when you multiply cosine x by its reciprocal?

• It becomes zero

• It becomes one

• It halves

• It doubles

What is the common factor identified in the expression 4 sin^2 x + 4 cos^2 x?

• 2

• 4

• sin x

• cos x

Which trigonometric identity is used to simplify sin^2 x + cos^2 x?

• Tangent identity

• Secant identity

• Pythagorean identity

• Cotangent identity

What is the final simplified form of the given trigonometric expression?

• 14

• 28

• 1

• 7

What is the result of simplifying 7 * 4 sin^2 x + 4 cos^2 x?

• 1

• 7

• 14

• 28

What is the purpose of factoring out common terms in an expression?

• To simplify the expression

• To make the expression more complex

• To change the trigonometric identities

• To increase the number of terms