Understanding Double Angle Identities

What is the main challenge when dealing with cosine double angle identities?

• There is only one formula to use.

• It is the same as the sine double angle identity.

• It does not exist in trigonometry.

• There are multiple formulas to choose from.

Why is the sine double angle identity considered easier than the cosine double angle identity?

• It is the same as the tangent double angle identity.

• It is not used in trigonometry.

• It has only one formula.

• It has multiple formulas.

Which identity is characterized by a number followed by sine and cosine?

• Reciprocal identities

• Quotient identities

• Sine double angle identity

• Pythagorean identities

What is the formula for sine double angle?

• sin(2θ) = 2cos²θ - 1

• sin(2θ) = 1 - 2sin²θ

• sin(2θ) = 2sinθcosθ

• sin(2θ) = sin²θ - cos²θ

How do you modify the sine double angle formula to match a problem with a coefficient of 14?

• Multiply the entire formula by 7

• Add 7 to the entire formula

• Subtract 7 from the entire formula

• Divide the entire formula by 7

What is the result of multiplying the sine double angle formula by 7?

• 14sin(2θ)

• 14sinθcosθ

• 7sin(2θ)

• 7sinθcosθ

What substitution is made to the angle theta in the problem-solving process?

• Theta is replaced by 12x

• Theta is replaced by 3x

• Theta is replaced by 2x

• Theta is replaced by 6x

What is the final expression for 14sin(6x)cos(6x) in terms of sine?

• 7sin(12x)

• 14sin(6x)

• 7sin(6x)

• 14sin(12x)

What is the purpose of replacing theta with 6x in the formula?

• To simplify the expression

• To complicate the expression

• To change the identity

• To match the problem's requirements

What does the expression 14sin(6x)cos(6x) simplify to?

• 7sin(12x)

• 14sin(12x)

• 7sin(6x)

• 14sin(6x)