AnswersGA-GSE Pre-CalculusInverse of a Function

Trigonometric Half Angle Identities Answers

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21
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Review the proof (not in order) of the identity .

Question illustration
A
1-3-2-4-5
B
1-3-4-2-5
C
1-4-2-3-5
D
1-4-3-2-5
22
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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
23

What is the exact value of tan

Question illustration
A
StartStartRoot StartFraction 2 minus StartRoot 2 EndRoot Over 2 + StartRoot 2 EndRoot EndFraction EndEndRoot
Option A
B
StartStartRoot StartFraction 2 + StartRoot 2 EndRoot Over 2 minus StartRoot 2 EndRoot EndFraction EndEndRoot
Option B
C
Negative StartStartRoot StartFraction 2 minus StartRoot 2 EndRoot Over 2 + StartRoot 2 EndRoot EndFraction EndEndRoot
Option C
D
Negative StartStartRoot StartFraction 2 + StartRoot 2 EndRoot Over 2 minus StartRoot 2 EndRoot EndFraction EndEndRoot
Option D
24

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

A
Left-brace StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction Right-brace
Option A
B
Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace
Option B
C
Left-brace StartFraction pi over 6 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Option C
D
Left-brace 0, StartFraction pi Over 3 EndFraction, pi, StartFraction 5 pi Over 3 EndFraction right-brace
Option D
25

For 0° ≤ x < 360°, what are the solutions to sin + cos(x) – 1 = 0 ?

Question illustration
A
{0°, 30°, 150°}
B
{0°, 60°, 300°}
C
{120°, 240°}
D
{210°, 330°}
26

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).

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