Answers2025-2026 FBISD - Precalculus A CRTrigonometric Double Angle Identities

Trigonometric Double Angle Identities Answers

10 verified answers
1
Free Preview

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

Question illustration
A
Negative StartFraction 2 StartRoot 8 EndRoot Over 7 EndFraction
Option A
B
Negative StartRoot 8 EndRoot
Option B
C
StartRoot 8 EndRoot
Option C
D
StartFraction 2 StartRoot 8 EndRoot Over 7 EndFraction
Option D
2
Free Preview

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

A
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).
Option A
B
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) + sine (x) sine (x), = cosine squared (x) + sine squared (x).
Option B
C
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), = sine (x) sine (x) + cosine (x) cosine (x), = sine squared (x) + cosine squared (x).
Option C
D
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), = sine (x) sine (x) minus cosine (x) cosine (x), = sine squared (x) minus cosine squared (x).
Option D
3

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

A
60° only
B
120° only
C
0° or 120°
D
60° or 180°
4

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

A
2
B
4
C
6
D
8
5

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

Question illustration
A
StartFraction 3 Over StartRoot 34 EndRoot EndFraction
Option A
B
StartFraction 6 Over StartRoot 34 EndRoot EndFraction
Option B
C
StartFraction 9 Over 34 EndFraction
Option C
D
StartFraction 30 Over 34 EndFraction
Option D
6

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

Question illustration
A
StartFraction 7 Over StartRoot 53 EndRoot EndFraction
Option A
B
StartFraction 14 Over StartRoot 53 EndRoot EndFraction
Option B
C
StartFraction 28 Over 53 EndFraction
Option C
D
StartFraction 49 Over 53 EndFraction
Option D
7

Which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over cosine (2 x) EndFraction
Option A
B
StartFraction 1 Over sine (2 x) EndFraction
Option B
C
Cosine (2 x)
Option C
D
Sine (2 x)
Option D
8

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

Question illustration
A
Negative StartFraction 14 Over 25 EndFraction
Option A
B
Negative StartFraction 7 Over 25 EndFraction
Option B
C
StartFraction 7 Over 25 EndFraction
Option C
D
StartFraction 14 Over 25 EndFraction
Option D
9

Simplify

Question illustration
A
StartFraction 2 sine (x) cosine (x) Over cosine (x) minus sine (x) EndFraction
Option A
B
StartFraction 2 sine (x) cosine (x) Over sine (x) minus cosine (x) EndFraction
Option B
C
cos(x) + sin(x)
D
cos(x) – sin(x)
10

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

Question illustration
A
In step 1, cos(2x) is equal to cos2(x) + sin2(x).
B
In step 2, sin2(x) should have been replaced with 1 + cos2(x).
C
In step 3, cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).
D
In step 4, 2cos2(x) – 1 should be 1 – 2cos2(x).

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Trigonometric Double Angle Identities

Quiz
25 verified answers

Angles and Trigonometric Functions

Quiz
10 verified answers

Monomial Functions

Trigonometric Double Angle Identities Answers —…