Q. If sin A = 0.6, what is the value of cos A?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
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Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin A = 0.6, what is the value of tan A?
A.
0.8
B.
1.2
C.
0.75
D.
1.5
Show solution
Solution
Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.
Correct Answer:
B
— 1.2
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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
Show solution
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 are the possible values of A in the range [0°, 360°]?
A.
30°, 150°
B.
45°, 135°
C.
60°, 300°
D.
90°, 270°
Show solution
Solution
sin A = 1/2 at A = 30° and A = 150°.
Correct Answer:
A
— 30°, 150°
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Q. If sin A = 1/2, what is the value of A in degrees?
Show solution
Solution
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 A in radians?
A.
π/6
B.
π/4
C.
π/3
D.
π/2
Show solution
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 A?
A.
45°
B.
30°
C.
60°
D.
90°
Show solution
Solution
The angle A for which sin A = 1/√2 is A = 45°.
Correct Answer:
A
— 45°
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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 = 3/5, what is the value of cos A?
A.
4/5
B.
3/5
C.
5/4
D.
1/2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
Correct Answer:
A
— 4/5
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Q. If sin A = 4/5, what is the value of tan A?
A.
3/4
B.
4/3
C.
5/4
D.
5/3
Show solution
Solution
Using the identity tan A = sin A / cos A, we find cos A = 3/5, thus tan A = (4/5) / (3/5) = 4/3.
Correct Answer:
B
— 4/3
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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 sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?
A.
sin(2x) = sin(x) + cos(x)
B.
sin(2x) = 2sin(x)cos(x)
C.
sin(2x) = sin^2(x) - cos^2(x)
D.
sin(2x) = 2sin^2(x)
Show solution
Solution
The double angle formula for sine is sin(2x) = 2sin(x)cos(x).
Correct Answer:
B
— sin(2x) = 2sin(x)cos(x)
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Q. If sin(2θ) = 2sin(θ)cos(θ), what is this identity called?
A.
Pythagorean Identity
B.
Double Angle Identity
C.
Sum Formula
D.
Product Formula
Show solution
Solution
This is known as the Double Angle Identity for sine.
Correct Answer:
B
— Double Angle Identity
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Q. If sin(x) = 0, what are the possible values of x?
A.
nπ
B.
nπ/2
C.
nπ + π/2
D.
nπ + π
Show solution
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
Show solution
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.
∞
Show solution
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
Show solution
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
Show solution
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
Show solution
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
Show solution
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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