Q. If cos B = 0.6, what is the value of sin B?
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A.
0.8
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B.
0.6
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C.
0.4
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D.
0.2
Solution
Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.
Correct Answer: A — 0.8
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Q. If cos B = 5/13, what is the value of sin B?
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A.
12/13
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B.
5/13
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C.
13/5
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D.
3/5
Solution
Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.
Correct Answer: A — 12/13
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Q. If cos C = 0.5, what is the value of angle C in degrees?
Solution
The angle C for which cos C = 0.5 is 60°.
Correct Answer: B — 60
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Q. If cot D = 3/4, what is the value of sin D?
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A.
3/5
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B.
4/5
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C.
5/3
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D.
5/4
Solution
cot D = 3/4 implies tan D = 4/3. Therefore, sin D = 4/5 (using the identity sin²D + cos²D = 1).
Correct Answer: A — 3/5
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Q. If sin 2A = 2 sin A cos A, what is the value of sin 2A when sin A = 1/2?
Solution
Using the double angle formula, sin 2A = 2(1/2)(√(1 - (1/2)²)) = 2(1/2)(√(3/4)) = 1.
Correct Answer: B — 1
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Q. If sin A = 1/√2, what is the value of tan A?
Solution
tan A = sin A / cos A = (1/√2) / (1/√2) = 1.
Correct Answer: A — 1
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Q. If sin C = 0.8, what is the value of cos C?
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A.
0.6
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B.
0.8
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C.
0.4
-
D.
0.2
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 θ = 0.8, what is the value of cos θ?
-
A.
0.6
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B.
0.8
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C.
0.4
-
D.
0.2
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. What is the value of sin(180° - θ)?
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A.
sin θ
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B.
cos θ
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C.
tan θ
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D.
sec θ
Solution
Using the identity, sin(180° - θ) = sin θ.
Correct Answer: A — sin θ
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