Trigonometric Functions and Identities

The video tutorial explains how to simplify a trigonometric expression by converting terms to sines and cosines. It demonstrates finding a common denominator, factoring, and simplifying the expression to its final form, which is tangent x times sine x.

What is the first step in simplifying a trigonometric expression?

• Multiply by the reciprocal

• Factor out common terms

• Convert everything to sines and cosines

• Find the least common denominator

How is cotangent x expressed in terms of sine and cosine?

• Cosine squared x divided by sine squared x

• Sine squared x divided by cosine squared x

• Cosine x divided by sine x

• Sine x divided by cosine x

What is the least common denominator when combining terms with sine and cosine?

• Cosine x

• Sine x

• Cosine squared x

• Sine squared x

What common factor is found in the numerator during simplification?

• Tangent x

• Cosine x

• Sine x

• Cotangent x

What is the purpose of factoring out common terms in the numerator?

• To eliminate the denominator

• To change the expression's value

• To simplify the expression

• To increase the expression's complexity

What operation is equivalent to dividing by a fraction?

• Adding the reciprocal

• Multiplying by the reciprocal

• Subtracting the reciprocal

• Dividing by the reciprocal

What is the result of simplifying the expression sine x plus cosine x over cosine x times sine x plus cosine x?

• Sine squared x divided by cosine x

• Sine x times tangent x

• Cosine squared x divided by sine x

• Tangent x times cosine x

How can sine x divided by cosine x be rewritten?

• Cosecant x

• Tangent x

• Cotangent x

• Secant x

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

• Sine squared x times cosine x

• Sine x times cosine x

• Tangent x times sine x

• Cosine x times tangent x

Which trigonometric identity is used to simplify sine x divided by cosine x?

• Tangent x

• Secant x

• Cosecant x

• Cotangent x