AnswersPrecalculusTrigonometric Difference Identities

Trigonometric Difference Identities — Unit test Answers

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What is expressed as a single trigonometric ratio?

Question illustration
A
–tan(20°)
B
–tan(5°)
C
tan(5°)
D
tan(20°)
2
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According to your graphing calculator, what is the approximate solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is greater than equal to 0 but less than 1.3280
Option A
B
x is greater than equal to 0 but less than 1.6985
Option B
C
x is greater than equal to 0 but less than 1.9182
Option C
D
x is greater than equal to 0 but less than 2.4534
Option D
3

What is the exact value of

Question illustration
A
StartFraction 1 Over 2 + StartRoot 3 EndRoot EndFraction
Option A
B
StartFraction 1 Over StartRoot 3 EndRoot EndFraction
Option B
C
StartFraction 3 Over StartRoot 3 EndRoot EndFraction
Option C
D
StartFraction 1 Over 2 minus StartRoot 3 EndRoot EndFraction
Option D
4

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.

Question illustration
A
0 seconds
B
1.38 seconds
C
4.62 seconds
D
8 seconds
5

What is the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is greater than equal to 0 but less than StartFraction 3pi over 2 EndFraction
Option A
B
and
Option B
C
and
Option C
D
x is greater than StartFraction 3pi over 2 EndFraction but less than equal to 2pi
Option D
6

Which expression is equivalent to cos(103°)cos(54°) – sin(103°)sin(54°)?

A
sin(49°)
B
cos(49°)
C
sin(157°)
D
cos(157°)
7

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

Question illustration
A
{0°, 60°, 300°}
B
{0°,120°, 240°}
C
{60°, 180°, 300°}
D
{120°,180°, 240°}
8

Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order.

Question illustration
A
4, 3, 5, 1, 2
B
4, 5, 3, 1, 2
C
3, 4, 5, 1, 2
D
3, 4, 1, 5, 2
9

Solve: over the interval .

Question illustration
A
StartFraction pi Over 2 EndFraction
Option A
B
StartFraction 2 pi Over 3 EndFraction
Option B
C
StartFraction 3 pi Over 4 EndFraction
Option C
D
StartFraction 5 pi Over 6 EndFraction
Option D
10

Which is equivalent to ? Give your answer in radians.

Question illustration
A
0
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
11

Which expression is equivalent to tan(x – )?

Question illustration
A
StartFraction tangent (x) minus tangent (pi) Over 1 minus (tangent (x) ) (tangent (pi) ) EndFraction
Option A
B
StartFraction tangent (x) minus tangent (pi) Over 1 + (tangent (x) ) (tangent (pi) ) EndFraction
Option B
C
StartFraction tangent (x) + tangent (pi) Over 1 minus (tangent (x) ) (tangent (pi) ) EndFraction
Option C
D
StartFraction tangent (x) + tangent (pi) Over 1 + (tangent (x) ) (tangent (pi) ) EndFraction
Option D
12

Given: What is the value of ?

Question illustration
A
StartFraction StartRoot 15 EndRoot + 1 Over 1 minus StartRoot 15 EndRoot EndFraction
Option A
B
StartFraction negative StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction
Option B
C
StartFraction StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction
Option C
D
StartFraction negative StartRoot 15 EndRoot minus 1 Over 1 minus StartRoot 15 EndRoot EndFraction
Option D
13

Which shows all the exact solutions of ? Give your answer in radians.

Question illustration
A
and
Option A
B
and
Option B
C
, , , and
Option C
D
, , , and
Option D
14

What is the range of ?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
15

Review the proof.

Question illustration
A
step 2
B
step 4
C
step 6
D
step 8
16

Review the proof of .tan(A – B) =Step 1: Step 2: Step 3: Step 4:

Question illustration
A
cos(A)cos(B)
B
cos(A)sin(B)
C
sin(A)cos(B)
D
sin(A)sin(B)
17

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

Question illustration
A
Negative StartFraction 16 Over 25 EndFraction
Option A
B
Negative StartFraction 7 Over 25 EndFraction
Option B
C
StartFraction 7 Over 25 EndFraction
Option C
D
StartFraction 16 Over 25 EndFraction
Option D
18

In which of the following intervals does the trigonometric inequality always hold true?

Question illustration
A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
19

Which values represent solutions to the equation? where x [0, ]

Question illustration
A
{0,}
Option A
B
Left-brace 0, StartFraction pi Over 2 EndFraction, pi Right-brace
Option B
C
Left-brace, 0, pi, 2 pi Right-brace
Option C
D
Left-brace 0, StartFraction pi Over 2 EndFraction, pi StartFraction 3 pi Over 2 EndFraction Right-brace
Option D
20

Which expression is equivalent to (1 + cos(x))2?

Question illustration
A
sin(x)
B
1 – cos(x)
C
1 – cos2(x)
D
(1 + cos(x))(sin(x))

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