AnswersCUSD Advanced Math B 5.0Test

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Which expression is equivalent to ?

Question illustration
A
tan(x)
B
–tan(x)
C
StartFraction 1 Over cosine (x) EndFraction
Option C
D
Negative StartFraction 1 Over cosine (x) EndFraction
Option D
2
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What is the value of 1 − 2sin2(105°)?

A
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option A
B
Negative one-half
Option B
C
One-half
Option C
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option D
3

Review the diagram of the unit circle.

Question illustration
A
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus 1) squared minus (sine (u) minus 0) squared EndRoot
Option A
B
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (negative v) minus 1) squared + (sine (negative v) minus 0) squared EndRoot
Option B
C
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus cosine (negative v) ) squared + (sine (u) minus sine (negative v)) squared
Option C
D
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u + v) minus cosine (u) ) squared + (sine (u + v) minus sine (u)) squared EndRoot
Option D
4

Review the proof of cos(A - B) = cosAcosB + sinAsinB.Step 1: Step 2: Step 3: Step 4: Step 5:Step 6:Step 7:

Question illustration
A
1 and 1
B
2 and 1
C
(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))
D
(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))
5

What is the exact value of tan ?

Question illustration
A
Negative 2 minus StartRoot 3 EndRoot
Option A
B
Negative 2 + StartRoot 3 EndRoot
Option B
C
1 minus StartRoot 3 EndRoot
Option C
D
1 + StartRoot 3 EndRoot
Option D
6

What are the solutions to the equation over the interval [0, 2]?

Question illustration
A
only
Option A
B
only
Option B
C
only
Option C
D
StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 7 pi Over 6 EndFraction and StartFraction 11 pi Over 6 EndFraction
Option D
7

Which shows a correct simplification of sin(x + )?

Question illustration
A
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · 1 + cos(x) · 0= sin(x)
Option A
B
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · 1 – sin(x) · 0= cos(x)
Option B
C
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · –1 + cos(x) · 0= –sin(x)
Option C
D
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · –1 – sin(x) · 0= –cos(x)
Option D
8

Read the proof.

Question illustration
A
tangent double angle identity
Option A
B
tangent sum identity
Option B
C
tangent double angle identity
Option C
D
tangent sum identity
Option D
9

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

A
30° only
B
90° only
C
30° or 150°
D
30°, 90°, or 150°
10

Which expression is equivalent to ?

Question illustration
A
Cosine (negative StartFraction pi Over 3 EndFraction)
Option A
B
Sine (negative StartFraction pi Over 3 EndFraction)
Option B
C
Cosine (StartFraction pi Over 2 EndFraction)
Option C
D
Sine (StartFraction pi Over 2 EndFraction)
Option D
11

What is the exact value of tan(195°)?

A
StartFraction StartRoot 3 EndRoot + 1 Over 1 minus StartRoot 3 EndRoot EndFraction
Option A
B
StartFraction StartRoot 3 EndRoot minus 3 Over 3 + StartRoot 3 EndRoot EndFraction
Option B
C
StartFraction StartRoot 3 EndRoot minus 1 Over 1 + StartRoot 3 EndRoot EndFraction
Option C
D
StartFraction StartRoot 3 EndRoot + 3 Over 3 minus StartRoot 3 EndRoot EndFraction
Option D
12

For what values of x is the trigonometric equation tan(x − 180°) − sin(x − 180°) = 0, where 0 ≤ x < 360°, true?

A
{0°, 90°}
B
{0°, 180°}
C
{90°, 180°}
D
{90°, 270°}

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