Section 9.3: Double-Angle, Half-Angle, and Reduction Formulas

What is the double-angle formula for sine?

• sin(2θ) = 2sinθcosθ

• sin(2θ) = sin^2θ - cos^2θ

• sin(2θ) = 1 - 2sin^2θ

• sin(2θ) = 2tanθ / (1 + tan^2θ)

Which formula represents the cosine double-angle identity?

• cos(2θ) = cos^2θ - sin^2θ

• cos(2θ) = 2cos^2θ - 1

• cos(2θ) = 1 - 2sin^2θ

• All of the above

How is the tangent of a double angle expressed using the tangent of the angle itself?

• tan(2θ) = 2tanθ / (1 - tan^2θ)

• tan(2θ) = sin(2θ) / cos(2θ)

• tan(2θ) = 2 / tanθ

• tan(2θ) = 1 - 2tanθ

What is the reduction formula for sin^2(θ)?

• sin^2(θ) = sin(2θ) / 2

• sin^2(θ) = 1 - cos(2θ) / 2

• sin^2(θ) = (1 - cos(2θ)) / 2

• sin^2(θ) = 2sin(θ)cos(θ)

Using the half-angle identities, how is sin(α/2) expressed?

• sin(α/2) = ±sqrt((1 + cosα) / 2)

• sin(α/2) = 1 - cosα

• sin(α/2) = sinα / 2

• sin(α/2) = ±sqrt((1 - cosα) / 2)

What is the correct expression for cos(α/2) using half-angle identities?

• cos(α/2) = ±sqrt((1 + cosα) / 2)

• cos(α/2) = 1 + cosα

• cos(α/2) = ±sqrt((1 - cosα) / 2)

• cos(α/2) = cosα / 2

How is tan(α/2) derived from the half-angle formulas?

• tan(α/2) = ±(1 - cosα) / (1 + cosα)

• tan(α/2) = ±(1 + cosα) / (1 - cosα)

• tan(α/2) = sinα / (1 + cosα)

• tan(α/2) = (1 - cosα) / sinα

What does the power-reducing formula for cos^2(θ) state?

• cos^2(θ) = (1 + cos(2θ)) / 2

• cos^2(θ) = 1 - sin^2(θ)

• cos^2(θ) = 2cos^2(θ) - 1

• cos^2(θ) = cos(2θ) / 2

Which identity verifies 1 + sin(2θ) = (sinθ + cosθ)^2?

• Double-angle identity for cosine

• Pythagorean identity

• Sum of squares identity

• Double-angle identity for sine

What is the correct expression for the tangent of a double angle using only the tangent of the angle?

• tan(2θ) = 2 / tanθ

• tan(2θ) = tanθ / 2

• tan(2θ) = 2tanθ / (1 + tan^2θ)

• tan(2θ) = 2tanθ / (1 - tan^2θ)