AnswersPrecalculusTrigonometric Difference Identities

Trigonometric Difference Identities Answers

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Given: < A < and < B < What is tan(A – B)?

Question illustration
A
StartFraction 5 + 12 StartRoot 13 EndRoot Over 12 minus 5 StartRoot 13 EndRoot EndFraction
Option A
B
StartFraction 12 minus 5 StartRoot 13 EndRoot Over 5 + 12 StartRoot 13 EndRoot EndFraction
Option B
C
StartFraction 12 + 5 StartRoot 13 EndRoot Over negative 5 + 12 StartRoot 13 EndRoot EndFraction
Option C
D
StartFraction negative 5 + 12 StartRoot 13 EndRoot Over 12 + 5 StartRoot 13 EndRoot EndFraction
Option D
2
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Review the steps of the proof.Step 1: Step 2: Step 3: Step 4:

Question illustration
A
Step 2 should be the last step.
B
Step 3 should be the last step.
C
Steps 2 and 3 must be switched.
D
Steps 3 and 4 must be switched.
3

Review the proof of sin(A – B) = sinAcosB – cosAsinBsin(A – B) = Step 1: Step 2: Step 3: Step 4: = sinAcosB – cosAsinB

Question illustration
A
Step 3 should be step 1.
B
Step 4 should be step 1.
C
Steps 1 and 2 must be switched.
D
Steps 1 and 3 must be switched.
4

Which values are two of the possible solutions to the equation?

Question illustration
A
Left-brace StartFraction pi Over 20 EndFraction, StartFraction 3 pi Over 20 EndFraction right-brace
Option A
B
Left-brace StartFraction pi Over 4 EndFraction, StartFraction 7 pi Over 4 EndFraction right-brace
Option B
C
Left-brace StartFraction pi Over 4 EndFraction, StartFraction 7 pi Over 20 EndFraction right-brace
Option C
D
Left-brace StartFraction 5 pi Over 4 EndFraction, StartFraction 7 pi Over 4 EndFraction right-brace
Option D
5

What is the value of cos(15°)?

A
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 2 EndFraction
Option A
B
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
Option B
C
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option C
D
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
Option D
6

Review the steps of the proof of the identity .Step 1: = Step 2: = Step 3: = Step 4: = Step 5:

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4
7

Which values represent solutions to , where x [0, 2)?

Question illustration
A
Left-brace 0, pi right-brace
Option A
B
Left-brace 0, StartFraction 3 pi Over 2 EndFraction right-brace
Option B
C
Left-brace StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Option C
D
Left-brace pi, StartFraction 3 pi Over 2 EndFraction
Option D
8

Review the proof of the identity cos(π − A) = −cosA.cos(π − A)Step 1: = cosπcosA − sinAsinπStep 2: = (−1)(cosA) + (sinA)(0)Step 3: = −1cosA + (sinA)(0)Step 4: = −cosA + 0Step 5: = −cosA

A
step 1
B
step 2
C
step 3
D
step 4
9

Which expression is equivalent to cos(40°)cos(10°) + sin(40°)sin(10°)?

A
sin(40° – 10°)
B
cos(40° + 10°)
C
sin(40° + 10°)
D
cos(40° – 10°)
10

What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?

A
Negative one-half
Option A
B
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option B
C
One-half
Option C
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option D
11

During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function , where x is the time in hours since 11:00 p.m.What is the height of the water at 2:15 a.m.?

Question illustration
A
0.22 feet below the marker
B
0.07 feet below the marker
C
1.26 feet above the marker
D
1.39 feet above the marker
12

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

Question illustration
A
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) minus 1
Option A
B
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) + 7
Option B
C
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) minus 1
Option C
D
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) + 7
Option D
13

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

Question illustration
A
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).
Option A
B
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).
Option B
C
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).
Option C
D
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).
Option D
14

Review the graph.

Question illustration
A
y = –3cos(x)
B
y = –3sin(x)
C
y = 3cos(x)
D
y = 3sin(x)
15

Which is an x-intercept of the graph of the function ?

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
16

A particle travels in a circle around a fixed point at 16 revolutions per minute. The linear velocity of the particle is 240π inches per minute.What is the distance, in inches, between the particle and the fixed point?

A
3.75
B
7.5
C
15
D
30
17

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

Question illustration
A
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option A
B
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option B
C
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option C
D
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option D
18

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

Question illustration
A
3.2
B
5.6
C
6.4
D
13.0
19

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

A
50 feet
B
feet
Option B
C
100 feet
D
feet
Option D
20

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D

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