Trigonometric Double Angle Identities

Question 1

What is the value of 2cos2(105⁰) − 1?

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/52b511b585bbdb4d33aeeabadd6b2b85.png

Question 2

If sin(x) = and cos(x) > 0, what is tan(2x)?

Revolt · Accepted Answer

Negative StartFraction 4 StartRoot 2 EndRoot Over 7 EndFraction

Question 3

What are the correct justifications, listed in proper order?

Revolt · Accepted Answer

Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity

Question 4

Over the interval [0, 2π), what are the solutions to cos(2x) = cos(x)? Check all that apply.

Revolt · Accepted Answer

0; StartFraction 2 pi Over 3 EndFraction; StartFraction 4 pi Over 3 EndFraction

Question 5

The table shows the derivation of cos(2x). Select the correct reason for each step. Reason 1 is . Reason 2 is . Reason 3 is .

Revolt · Accepted Answer

Addition; Selection 1: Addition; Selection 2: Cosine Sum Identity; Selection 3: Simplify

Question 6

Question 11

Revolt · Accepted Answer

Cosine Sum Identity

Question 7

Question 12

Revolt · Accepted Answer

Simplify

Question 8

The table shows the derivation of tan(2x). Select the correct reason for each step. Reason 1 is . Reason 2 is . Reason 3 is .

Revolt · Accepted Answer

Addition; Reason 1 is .: Addition; Reason 2 is .: Tangent Sum Identity; Reason 3 is .: Simplify

Question 9

Double Angle Identity✔ Tangent Sum IdentityQuotient Identity for Tangent

Revolt · Accepted Answer

Tangent Sum Identity

Question 10

Quotient Identity for TangentTangent Sum Identity✔ Simplify

Revolt · Accepted Answer

Simplify

Trigonometric Double Angle Identities Answers