AnswersPrecalculusTrigonometric Sum Identities

Trigonometric Sum Identities — Unit test Answers

25 verified answers2 views
1
Free Preview

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
2
Free Preview

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
3

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))
4

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
5

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
6

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
7

Review the incomplete steps in the derivation of the tangent sum identity.Which action can be taken to the expression in Step 3 to give an expression for Step 4?

Question illustration
A
divide both the numerator and denominator by sin(x)sin(y)
B
divide both the numerator and denominator by sin(x)cos(y)
C
divide both the numerator and denominator by cos(x)sin(y)
D
divide both the numerator and denominator by cos(x)cos(y)
8

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
9

What is expressed as a single trigonometric ratio?

Question illustration
A
–tan(20°)
B
–tan(5°)
C
tan(5°)
D
tan(20°)
10

What is the exact value of sin(264°)cos(6°) + cos(264°)sin(6°)?

A
–1
B
Negative one-half
Option B
C
0
D
1
11

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
12

Let where 0° ≤ x ≤ 180°. What are the possible values for x?

Question illustration
A
45° only
B
135° only
C
45° or 225°
D
135° or 315°
13

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°)
14

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
15

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
16

What is the range of ?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
17

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
18

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)
19

Review the proof.

Question illustration
A
step 2
B
step 4
C
step 6
D
step 8
20

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°}

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Unit Test

Quiz
25 verified answers

Unit Test

Quiz
25 verified answers

Unit Test

Trigonometric Sum Identities — Unit test Answers…