Trigonometric Double Angle Identities

Question 1

Which derivation correctly uses the cosine sum identity to prove the cosine double angle identity?

Revolt · Accepted Answer

A 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries cosine (2 x) = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x).

Question 2

What is the value of 2cos2(75°) – 1?

Revolt · Accepted Answer

Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Question 3

Which expression is equal to ?

Revolt · Accepted Answer

Sine StartFraction pi Over 5 EndFraction

Question 4

Suppose where . What is the value of tan(2x)?

Revolt · Accepted Answer

StartFraction 2 StartRoot 8 EndRoot Over 7 EndFraction

Question 5

Consider the derivation of an alternate form of the cosine double angle identity.

Revolt · Accepted Answer

In step 3, cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).

Question 6

Consider the derivation of sin(2x).

Revolt · Accepted Answer

Step 3 should read = 2sin(x)cos(x).

Question 7

Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x?

Revolt · Accepted Answer

Left-brace 0, StartFraction pi Over 3 EndFraction, pi, StartFraction 5 pi Over 3 EndFraction right-brace

Question 8

Which expression is equivalent to cos(4x)?

Revolt · Accepted Answer

2(2cos2(x) – 1)2 – 1

Question 9

Suppose where 180° < x < 270°. What is the value of sin(2x)?

Revolt · Accepted Answer

StartFraction 28 Over 53 EndFraction

Question 10

Let cos(2x) – cos(x) = 0, where 0° ≤ x ≤ 180°. What are the possible values for x?

Revolt · Accepted Answer

0° or 120°

Trigonometric Double Angle Identities Answers

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