Section 9.4: Sum-to-Product and Product-to-Sum Formulas

What is the formula for expressing the product of cosines as a sum?

• cos(α)cos(β) = 1/2 [cos(α−β) + cos(α+β)]

• cos(α)cos(β) = cos(α+β) - cos(α−β)

• cos(α)cos(β) = sin(α+β) + sin(α−β)

• cos(α)cos(β) = 1/2 [sin(α−β) - sin(α+β)]

How can you express the product of sine and cosine as a sum?

• sin(α)cos(β) = 1/2 [cos(α−β) - cos(α+β)]

• sin(α)cos(β) = cos(α+β) + cos(α−β)

• sin(α)cos(β) = sin(α+β) - sin(α−β)

• sin(α)cos(β) = 1/2 [sin(α+β) + sin(α−β)]

What is the result of expressing the product of sines in terms of cosine?

• sin(α)sin(β) = sin(α+β) - sin(α−β)

• sin(α)sin(β) = cos(α+β) + cos(α−β)

• sin(α)sin(β) = 1/2 [sin(α+β) + sin(α−β)]

• sin(α)sin(β) = 1/2 [cos(α−β) - cos(α+β)]

Which formula represents the sum-to-product identity for sine?

• sin(α) + sin(β) = 2cos((α+β)/2)sin((α−β)/2)

• sin(α) + sin(β) = cos((α+β)/2) + cos((α−β)/2)

• sin(α) + sin(β) = sin((α+β)/2) + sin((α−β)/2)

• sin(α) + sin(β) = 2sin((α+β)/2)cos((α−β)/2)

How do you express the difference of cosines as a product?

• cos(α) - cos(β) = sin((α+β)/2) - sin((α−β)/2)

• cos(α) - cos(β) = 2sin((α+β)/2)cos((α−β)/2)

• cos(α) - cos(β) = -2sin((α+β)/2)sin((α−β)/2)

• cos(α) - cos(β) = cos((α+β)/2) - cos((α−β)/2)

What is the correct expression for the sum of cosines in terms of product?

• cos(α) + cos(β) = 2sin((α+β)/2)sin((α−β)/2)

• cos(α) + cos(β) = sin((α+β)/2) + sin((α−β)/2)

• cos(α) + cos(β) = cos((α+β)/2) + cos((α−β)/2)

• cos(α) + cos(β) = 2cos((α+β)/2)cos((α−β)/2)

Using the product-to-sum formulas, how can you express cos(3θ)cos(5θ)?

• 1/2 [sin(2θ) - sin(8θ)]

• 1/2 [sin(2θ) + sin(8θ)]

• 1/2 [cos(2θ) - cos(8θ)]

• 1/2 [cos(2θ) + cos(8θ)]

What is the formula for expressing the product of a sine and a cosine as a sum, using specific angles?

• sin(4θ)cos(2θ) = 1/2 [sin(6θ) - sin(2θ)]

• sin(4θ)cos(2θ) = 1/2 [cos(6θ) + cos(2θ)]

• sin(4θ)cos(2θ) = 1/2 [cos(6θ) - cos(2θ)]

• sin(4θ)cos(2θ) = 1/2 [sin(6θ) + sin(2θ)]

How can the difference of sines be expressed as a product?

• sin(4θ) - sin(2θ) = 2cos(3θ)sin(θ)

• sin(4θ) - sin(2θ) = 2sin(θ)cos(3θ)

• sin(4θ) - sin(2θ) = 2cos(θ)sin(3θ)

• sin(4θ) - sin(2θ) = 2sin(3θ)cos(θ)

What is the sum-to-product formula for the sum of two sine functions?

• sin(3θ) + sin(θ) = 2sin(θ)cos(2θ)

• sin(3θ) + sin(θ) = 2cos(2θ)sin(θ)

• sin(3θ) + sin(θ) = 2sin(2θ)cos(θ)

• sin(3θ) + sin(θ) = 2cos(θ)sin(2θ)