Power Reducing Formulas in Trigonometry

The video tutorial covers the derivation and application of power reducing formulas for trigonometric functions. It begins with the derivation of formulas for sine squared and cosine squared using double angle identities. The tutorial then explains how to derive the power reducing formula for tangent squared. It demonstrates the simplification of trigonometric expressions using these formulas, including an example of reducing sine to the fourth power. The tutorial emphasizes the importance of these formulas in simplifying expressions by reducing the exponents of trigonometric functions.

What is the power reducing formula for sine squared derived from the double angle formula for cosine?

• cosine 2θ divided by 2

• 2 - cosine 2θ divided by 2

• 1 - cosine 2θ divided by 2

• 1 + cosine 2θ divided by 2

How do you derive the power reducing formula for cosine squared?

• By dividing both sides of the equation by 2

• By multiplying both sides of the equation by 2

• By adding 1 to both sides of the equation and dividing by 2

• By subtracting 1 from both sides of the equation and dividing by 2

What is the power reducing formula for tangent squared?

• 1 - sine 2θ divided by 1 + sine 2θ

• 1 - cosine 2θ divided by 1 + cosine 2θ

• 1 + sine 2θ divided by 1 - sine 2θ

• 1 + cosine 2θ divided by 1 - cosine 2θ

How can the expression 4 sine squared x cosine squared x be simplified using power reducing formulas?

• 1 + cosine 2x divided by 2

• 1 - cosine 4x divided by 2

• 1 + cosine 4x divided by 2

• 1 - cosine 2x divided by 2

What happens to the angle when using the power reducing formula on cosine squared?

• The angle is tripled

• The angle is halved

• The angle is doubled

• The angle remains the same

What is the first step in reducing 16 sine to the fourth x using power reducing formulas?

• Rewrite sine to the fourth as cosine squared squared

• Rewrite sine to the fourth as tangent squared squared

• Rewrite sine to the fourth as sine cubed squared

• Rewrite sine to the fourth as sine squared squared

After applying the power reducing formula, what is the next step in simplifying 16 sine to the fourth x?

• Multiply by 8

• Divide by 4

• Subtract 4

• Add 4

What is the result of foiling the expression 1 - cosine 2x times 1 - cosine 2x?

• 1 - 2 cosine 2x + cosine squared 2x

• 1 + 2 cosine 2x + cosine squared 2x

• 1 - cosine 2x + cosine squared 2x

• 1 + cosine 2x + cosine squared 2x

What is the final simplified form of the expression 16 sine to the fourth x?

• 4 cosine 4x + 8 cosine 2x + 6

• 2 cosine 4x + 8 cosine 2x + 6

• 4 cosine 4x - 8 cosine 2x + 6

• 2 cosine 4x - 8 cosine 2x + 6

What is the purpose of using power reducing formulas in trigonometry?

• To solve trigonometric equations directly

• To convert trigonometric functions to exponential form

• To simplify trigonometric expressions by reducing powers

• To increase the power of trigonometric functions