Q. If sin A = 0, what is the value of A? (2019)
A.
0°
B.
90°
C.
180°
D.
360°
Show solution
Solution
Sin A = 0 at A = 0°, 180°, and 360°. The principal value is 0°.
Correct Answer:
A
— 0°
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Q. If sin A = 0.6, what is the value of cos A to two decimal places?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
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Solution
Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - 0.36) = √(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin A = 0.8, what is the value of tan A?
A.
0.6
B.
1.2
C.
1.5
D.
0.8
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Solution
Using the identity tan A = sin A / cos A. First, find cos A using cos A = √(1 - sin² A) = √(1 - 0.64) = 0.6. Therefore, tan A = 0.8 / 0.6 = 1.3333, which is approximately 1.2.
Correct Answer:
B
— 1.2
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Q. If sin A = 1/2, what is the value of A in radians?
A.
π/6
B.
π/4
C.
π/3
D.
π/2
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Solution
The angle A for which sin A = 1/2 is π/6 radians.
Correct Answer:
A
— π/6
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Q. If sin A = 1/2, what is the value of A in the first quadrant?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
In the first quadrant, sin A = 1/2 corresponds to A = 30°.
Correct Answer:
A
— 30°
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Q. If sin A = 1/√2, what is the value of tan A?
Show solution
Solution
tan A = sin A / cos A = (1/√2) / (1/√2) = 1.
Correct Answer:
A
— 1
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Q. If sin A = 5/13, what is the value of cos A?
A.
12/13
B.
5/12
C.
13/5
D.
1/5
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Solution
Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.
Correct Answer:
A
— 12/13
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Q. If sin C = 0.5, what is the value of cos C?
A.
√3/2
B.
1/2
C.
0.5
D.
√2/2
Show solution
Solution
Using the Pythagorean identity, cos C = √(1 - sin² C) = √(1 - 0.25) = √0.75 = √3/2.
Correct Answer:
A
— √3/2
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Q. If sin C = 0.8, what is the value of cos C?
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using the Pythagorean identity, cos C = √(1 - sin²C) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.
Correct Answer:
A
— 0.6
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Q. If sin x = 0.6, what is the value of cos x?
A.
0.8
B.
0.6
C.
0.4
D.
0.5
Show solution
Solution
Using the Pythagorean identity, cos x = √(1 - sin²x) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin θ = 0.8, what is the value of cos θ?
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using the Pythagorean identity, cos θ = √(1 - sin²θ) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.
Correct Answer:
A
— 0.6
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Q. If sin²A + cos²A = 1, what is sin²A when cos A = 0.6?
A.
0.36
B.
0.64
C.
0.76
D.
0.16
Show solution
Solution
Using the identity, sin²A = 1 - cos²A = 1 - (0.6)² = 1 - 0.36 = 0.64.
Correct Answer:
B
— 0.64
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Q. If sin²A + cos²A = 1, what is the value of sin²A when cos A = 0?
A.
0
B.
1
C.
1/2
D.
Undefined
Show solution
Solution
If cos A = 0, then sin²A = 1 - cos²A = 1 - 0 = 1.
Correct Answer:
B
— 1
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Q. If someone is 'barking up the wrong tree', what does it imply? (2019)
A.
They are mistaken about something
B.
They are very angry
C.
They are confused
D.
They are very happy
Show solution
Solution
'Barking up the wrong tree' means to pursue a mistaken or misguided course of action.
Correct Answer:
A
— They are mistaken about something
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Q. If someone is 'on cloud nine', what does it mean?
A.
They are very sad
B.
They are very happy
C.
They are confused
D.
They are busy
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Solution
'On cloud nine' means to be in a state of blissful happiness.
Correct Answer:
B
— They are very happy
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Q. If someone is 'under the weather', what does it imply? (2020)
A.
They are feeling sick
B.
They are feeling happy
C.
They are feeling confused
D.
They are feeling energetic
Show solution
Solution
'Under the weather' is an idiom that means someone is feeling ill or unwell.
Correct Answer:
A
— They are feeling sick
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Q. If someone is 'under the weather', what does it mean? (2021)
A.
Feeling sick
B.
Feeling happy
C.
Feeling confused
D.
Feeling energetic
Show solution
Solution
'Under the weather' means feeling ill or unwell.
Correct Answer:
A
— Feeling sick
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Q. If someone is said to 'burn the midnight oil', what does it mean? (2022)
A.
To work late into the night
B.
To waste resources
C.
To be very busy during the day
D.
To relax and take it easy
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Solution
'Burn the midnight oil' means to stay up late working or studying.
Correct Answer:
A
— To work late into the night
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Q. If someone is said to 'hit the nail on the head', what does it mean? (2019)
A.
To make a mistake
B.
To be very accurate or correct
C.
To cause a problem
D.
To be overly critical
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Solution
'Hit the nail on the head' means to describe exactly what is causing a situation or to be very accurate in one's assessment.
Correct Answer:
B
— To be very accurate or correct
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Q. If someone is said to 'let the cat out of the bag', what does it mean?
A.
To reveal a secret unintentionally
B.
To adopt a pet
C.
To be careless
D.
To be very happy
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Solution
'Let the cat out of the bag' means to accidentally reveal a secret.
Correct Answer:
A
— To reveal a secret unintentionally
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Q. If someone is said to 'spill the beans', what does it mean? (2021)
A.
To cook something poorly
B.
To reveal confidential information
C.
To waste resources
D.
To be overly generous
Show solution
Solution
'Spill the beans' means to reveal confidential information or secrets.
Correct Answer:
B
— To reveal confidential information
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Q. If someone is said to have 'a chip on their shoulder', what does it mean? (2021)
A.
They are feeling relaxed
B.
They are feeling angry or resentful
C.
They are feeling happy
D.
They are feeling indifferent
Show solution
Solution
'A chip on their shoulder' means to have a grudge or to be angry about something.
Correct Answer:
B
— They are feeling angry or resentful
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Q. If someone says they are 'on cloud nine', what does it mean? (2022)
A.
They are very happy
B.
They are confused
C.
They are in trouble
D.
They are busy
Show solution
Solution
'On cloud nine' is an idiom that signifies being in a state of extreme happiness.
Correct Answer:
A
— They are very happy
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Q. If tan θ = 1/√3, what is the value of sin θ?
A.
1/2
B.
√3/2
C.
1/√2
D.
√2/2
Show solution
Solution
Since tan θ = sin θ / cos θ, and tan θ = 1/√3, we can use the 30-60-90 triangle where sin θ = 1/2.
Correct Answer:
A
— 1/2
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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)
Show solution
Solution
A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25
Correct Answer:
B
— 30
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Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is A · B?
Show solution
Solution
A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25.
Correct Answer:
B
— 30
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Q. If the angle between two vectors A and B is 90 degrees, what is A · B?
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Solution
A · B = |A||B|cos(90°) = |A||B| * 0 = 0.
Correct Answer:
A
— 0
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Q. If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)
A.
50 m
B.
30 m
C.
20 m
D.
10 m
Show solution
Solution
Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.
Correct Answer:
A
— 50 m
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Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Show solution
Solution
Height = shadow * tan(angle) = 10 * tan(30) = 10 * (1/√3) ≈ 10 m.
Correct Answer:
B
— 10 m
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Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Show solution
Solution
Height = Shadow * tan(30) = 10√3 * (1/√3) = 10 m.
Correct Answer:
B
— 10 m
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