Trigonometry
Q. If cos(θ) = 0, what is the value of θ? (2017)
-
A.
0°
-
B.
90°
-
C.
180°
-
D.
270°
Solution
cos(90°) = 0, so θ = 90°
Correct Answer: B — 90°
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Q. If cos(θ) = 0.5, what is the value of θ in degrees? (2017)
-
A.
30°
-
B.
45°
-
C.
60°
-
D.
90°
Solution
cos(60°) = 0.5, so θ = 60°
Correct Answer: C — 60°
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Q. If cos(θ) = 0.5, what is the value of θ? (2020)
-
A.
0°
-
B.
30°
-
C.
60°
-
D.
90°
Solution
cos(60°) = 0.5, so θ = 60°.
Correct Answer: C — 60°
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Q. If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)
-
A.
0.4
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B.
0.5
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C.
0.6
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D.
0.8
Solution
sin²(θ) + cos²(θ) = 1; sin²(θ) = 1 - 0.6² = 0.64; sin(θ) = √0.64 = 0.8.
Correct Answer: A — 0.4
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Q. If cos(θ) = 1/2, what is θ in degrees?
-
A.
30°
-
B.
45°
-
C.
60°
-
D.
90°
Solution
cos(60°) = 1/2, so θ = 60°
Correct Answer: C — 60°
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Q. If sin(θ) = 0.5, what is θ in degrees? (2014)
-
A.
30°
-
B.
45°
-
C.
60°
-
D.
90°
Solution
sin(30°) = 0.5, so θ = 30°.
Correct Answer: A — 30°
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Q. If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)
-
A.
0.6
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B.
0.8
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C.
0.4
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D.
0.2
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
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D.
0.2
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°
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? (2023)
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A.
0°
-
B.
90°
-
C.
180°
-
D.
270°
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer: B — 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°
Solution
sin(30°) = 1/2, so θ = 30°.
Correct Answer: A — 30°
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Q. If sin(θ) = 1/√2, what is θ in degrees?
-
A.
30°
-
B.
45°
-
C.
60°
-
D.
90°
Solution
sin(45°) = 1/√2, so θ = 45°
Correct Answer: B — 45°
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Q. If tan(θ) = 1, what is the value of θ? (2020)
-
A.
0°
-
B.
30°
-
C.
45°
-
D.
60°
Solution
tan(45°) = 1, so θ = 45°.
Correct Answer: C — 45°
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Q. What is the value of cot(45°)?
Solution
cot(45°) = 1/tan(45°) = 1/1 = 1
Correct Answer: B — 1
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Q. What is the value of cot(90°)? (2018)
-
A.
0
-
B.
1
-
C.
undefined
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D.
∞
Solution
cot(90°) = 1/tan(90°) = 1/0 = undefined.
Correct Answer: C — undefined
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Q. What is the value of sec(0°)?
Solution
sec(0°) = 1/cos(0°) = 1/1 = 1
Correct Answer: B — 1
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Q. What is the value of sec(30°)? (2015)
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A.
√3/2
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B.
2/√3
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C.
2
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D.
√3
Solution
sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3 = √3
Correct Answer: D — √3
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Q. What is the value of sec(45°)? (2019)
Solution
sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.
Correct Answer: B — √2
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Q. What is the value of sin(45°)? (2016)
-
A.
1/√2
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B.
1/2
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C.
√3/2
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D.
1
Solution
sin(45°) = 1/√2
Correct Answer: A — 1/√2
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Q. What is the value of tan(0°)? (2018)
-
A.
0
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B.
1
-
C.
undefined
-
D.
∞
Q. What is the value of tan(90°)? (2022)
-
A.
0
-
B.
1
-
C.
undefined
-
D.
∞
Solution
tan(90°) is undefined.
Correct Answer: C — undefined
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