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

Authored by Julie Sullivan

Mathematics

University

CCSS covered

Used 3+ times

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

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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)

Tags

CCSS.HSF.TF.C.9

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSF.TF.C.9

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSF.TF.C.9

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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)

Tags

CCSS.HSF.TF.C.9

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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)

Tags

CCSS.HSF.TF.C.9

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSF.TF.C.9

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSF.TF.C.9

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