Q. If sin(x) = 0, what are the possible values of x?
A.
nπ
B.
nπ/2
C.
nπ + π/2
D.
nπ + π
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Solution
sin(x) = 0 at x = nπ, where n is any integer.
Correct Answer: A — nπ
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Q. If sin(x) = 0, what is the value of cos(x)?
A.
1
B.
0
C.
-1
D.
undefined
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Solution
If sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.
Correct Answer: A — 1
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Q. If sin(x) = 0, what is the value of tan(x)?
A.
0
B.
1
C.
undefined
D.
∞
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Solution
tan(x) = sin(x)/cos(x). If sin(x) = 0, then tan(x) is undefined when cos(x) = 0.
Correct Answer: C — undefined
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Q. If sin(x) = 0, what is the value of x?
A.
0
B.
π
C.
2π
D.
All of the above
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Solution
sin(x) = 0 at x = nπ, where n is any integer, hence all of the above.
Correct Answer: D — All of the above
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Q. If sin(x) = 1/2, what are the possible values of x in the interval [0, 2π)?
A.
π/6, 5π/6
B.
π/4, 3π/4
C.
π/3, 2π/3
D.
0, π
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Solution
The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.
Correct Answer: A — π/6, 5π/6
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Q. If sin(x) = 1/2, what are the possible values of x in [0, 2π]?
A.
π/6, 5π/6
B.
π/4, 3π/4
C.
0, π
D.
π/3, 2π/3
Show solution
Solution
sin(x) = 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π].
Correct Answer: A — π/6, 5π/6
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Q. If sin(x) = 1/2, what is the value of x in degrees?
Show solution
Solution
sin(30°) = 1/2, so x = 30°.
Correct Answer: A — 30
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Q. If sin(x) = 1/2, what is the value of x in the interval [0, 2π]?
A.
π/6
B.
5π/6
C.
7π/6
D.
11π/6
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Solution
The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.
Correct Answer: A — π/6
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Q. If sin(x) = 1/2, what is the value of x in the range [0, 2π]?
A.
π/6
B.
π/3
C.
5π/6
D.
7π/6
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Solution
x = π/6 and 5π/6.
Correct Answer: A — π/6
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Q. If sin(x) = 1/√2, what is cos(x)?
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.
Correct Answer: A — 1/√2
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Q. If sin(x) = 1/√2, what is tan(x)?
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Solution
tan(x) = sin(x)/cos(x) = (1/√2)/(1/√2) = 1.
Correct Answer: B — √2
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Q. If sin(x) = 1/√2, what is the value of cos(x)?
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Therefore, cos(x) = 1/√2.
Correct Answer: A — 1/√2
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Q. If sin(x) = 3/5, what is cos(x)?
A.
4/5
B.
3/5
C.
5/4
D.
1/5
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Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.
Correct Answer: A — 4/5
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Q. If sin(x) = 3/5, what is the value of cos(x)?
A.
4/5
B.
3/5
C.
5/4
D.
1/5
Show solution
Solution
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5.
Correct Answer: A — 4/5
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Q. If sin(α) = 0.6, what is the value of cos(α) using the identity?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
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Solution
Using sin^2(α) + cos^2(α) = 1, we find cos(α) = √(1 - 0.6^2) = √(1 - 0.36) = √0.64 = 0.8.
Correct Answer: A — 0.8
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Q. If sin(θ) = 0, what are the possible values of θ in the interval [0, 2π]?
A.
0, π
B.
0, 2π
C.
π/2, 3π/2
D.
π/4, 3π/4
Show solution
Solution
The angles where sin(θ) = 0 in the interval [0, 2π] are θ = 0 and θ = π.
Correct Answer: A — 0, π
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Q. If sin(θ) = 0, what are the possible values of θ?
A.
0°, 180°
B.
90°, 270°
C.
45°, 135°
D.
30°, 150°
Show solution
Solution
sin(θ) = 0 at θ = 0° and 180°.
Correct Answer: A — 0°, 180°
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Q. If sin(θ) = 0.5, what is θ in degrees? (2014)
A.
30°
B.
45°
C.
60°
D.
90°
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Solution
sin(30°) = 0.5, so θ = 30°.
Correct Answer: A — 30°
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Q. If sin(θ) = 0.6, what is the approximate value of θ in degrees? (2019)
A.
36.87°
B.
45°
C.
53.13°
D.
60°
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Solution
Using inverse sine, θ ≈ 36.87°
Correct Answer: C — 53.13°
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Q. If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6
Correct Answer: A — 0.6
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Q. If sin(θ) = 0.8, what is cos(θ)? (2022)
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.
Correct Answer: A — 0.6
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Q. If sin(θ) = 0.866, what is θ in degrees? (2020)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(60°) = √3/2 ≈ 0.866, so θ = 60°.
Correct Answer: C — 60°
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Q. If sin(θ) = 0.866, what is θ? (2022)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(60°) = √3/2 ≈ 0.866, so θ = 60°.
Correct Answer: C — 60°
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Q. If sin(θ) = 1, what is the value of θ in degrees? (2019)
A.
0°
B.
45°
C.
90°
D.
180°
Show solution
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer: C — 90°
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Q. If sin(θ) = 1, what is the value of θ? (2023)
A.
0°
B.
90°
C.
180°
D.
270°
Show solution
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer: B — 90°
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Q. If sin(θ) = 1, what is θ? (2023)
A.
0°
B.
30°
C.
90°
D.
180°
Show solution
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer: C — 90°
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Q. If sin(θ) = 1/2, what is the possible value of θ? (2022)
A.
30°
B.
60°
C.
90°
D.
45°
Show solution
Solution
sin(30°) = 1/2, so θ = 30°.
Correct Answer: A — 30°
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Q. If sin(θ) = 1/√2, what is cos(θ)? (2022)
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - (1/√2)²) = √(1/2) = √2/2
Correct Answer: C — √2/2
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Q. If sin(θ) = 1/√2, what is the value of cos(θ)?
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using the identity sin^2(θ) + cos^2(θ) = 1, we have cos^2(θ) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(θ) = ±1/√2.
Correct Answer: A — 1/√2
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Q. If sin(θ) = 1/√2, what is the value of θ in degrees?
A.
45°
B.
30°
C.
60°
D.
90°
Show solution
Solution
sin(θ) = 1/√2 at θ = 45°.
Correct Answer: A — 45°
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