Trigonometric Double Angle Identities

Question 1

Which expression is equal to ?

Revolt · Accepted Answer

Sine StartFraction pi Over 5 EndFraction

Question 2

Read the proof.

Revolt · Accepted Answer

sin(2x) = sin(x)cos(x) + sin(x)cos(x)

Question 3

Let tan(2x) + tan(x) = 0, where 0 ≤ x < 2π. How many possible solutions are there for x?

Revolt · Accepted Answer

6

Question 4

Which expression is equivalent to cos(4x)?

Revolt · Accepted Answer

2(2cos2(x) – 1)2 – 1

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

Which expression is equivalent to ?

Revolt · Accepted Answer

StartFraction 1 Over cosine (2 x) EndFraction

Question 7

Suppose and cos(x) < 0. What is the value of cos(2x)?

Revolt · Accepted Answer

Negative StartFraction 7 Over 25 EndFraction

Question 8

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

Revolt · Accepted Answer

StartFraction 28 Over 53 EndFraction

Question 9

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

Revolt · Accepted Answer

0° or 120°

Question 10

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

Trigonometric Double Angle Identities Answers