Q. If cos A = 5/13, what is the value of tan A?
A.
12/5
B.
5/12
C.
13/5
D.
5/13
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Solution
Using the identity tan A = sin A / cos A, we find sin A = √(1 - cos²A) = √(1 - (5/13)²) = 12/13. Thus, tan A = (12/13) / (5/13) = 12/5.
Correct Answer:
A
— 12/5
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Q. If cos B = 0.6, what is the value of sin B?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
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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?
A.
12/13
B.
5/13
C.
13/5
D.
3/5
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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?
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Solution
The angle C for which cos C = 0.5 is 60°.
Correct Answer:
B
— 60
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Q. If cot A = 3/4, what is the value of sin A?
A.
3/5
B.
4/5
C.
5/3
D.
5/4
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Solution
cot A = cos A/sin A = 3/4 implies sin A = 4/5 using the identity sin²A + cos²A = 1.
Correct Answer:
A
— 3/5
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Q. If cot D = 3/4, what is the value of sin D?
A.
3/5
B.
4/5
C.
5/3
D.
5/4
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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 cot θ = 1, what is the value of θ?
A.
0°
B.
45°
C.
90°
D.
180°
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Solution
cot θ = 1 implies tan θ = 1, which occurs at θ = 45°.
Correct Answer:
B
— 45°
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Q. If sin 2A = 2 sin A cos A, what is the double angle formula for cosine?
A.
cos 2A = cos²A - sin²A
B.
cos 2A = 2 sin A cos A
C.
cos 2A = sin²A - cos²A
D.
cos 2A = 1 - 2 sin²A
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Solution
The double angle formula for cosine is cos 2A = cos²A - sin²A.
Correct Answer:
A
— cos 2A = cos²A - sin²A
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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?
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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 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?
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Solution
sin 2(30°) = sin 60° = √3/2.
Correct Answer:
C
— √3/2
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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 tan A?
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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
Show solution
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 the value of sin²A when cos A = 0?
A.
0
B.
1
C.
1/2
D.
Undefined
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Solution
If cos A = 0, then sin²A = 1 - cos²A = 1 - 0 = 1.
Correct Answer:
B
— 1
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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
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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. What is the value of csc 30°?
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Solution
Cosecant is the reciprocal of sine. Since sin 30° = 1/2, csc 30° = 1 / (1/2) = 2.
Correct Answer:
A
— 2
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Q. What is the value of sin(180° - θ)?
A.
sin θ
B.
cos θ
C.
tan θ
D.
sec θ
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Solution
Using the identity, sin(180° - θ) = sin θ.
Correct Answer:
A
— sin θ
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Q. What is the value of tan(60°)?
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