Q. What is the value of sin(2θ) if sin(θ) = 1/√2?
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A.
1/√2
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B.
1
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C.
√2/2
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D.
√2
Solution
Using the double angle formula, sin(2θ) = 2sin(θ)cos(θ) = 2(1/√2)(1/√2) = 1.
Correct Answer: B — 1
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Q. What is the value of sin(2θ) in terms of sin θ?
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A.
2sin θ
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B.
2sin θcos θ
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C.
sin^2 θ
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D.
2sin^2 θ
Solution
Using the double angle formula, sin(2θ) = 2sin θcos θ.
Correct Answer: B — 2sin θcos θ
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Q. What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?
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A.
2sin(θ)cos(θ)
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B.
sin^2(θ) + cos^2(θ)
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C.
sin(θ) + cos(θ)
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D.
sin(θ)cos(θ)
Solution
Using the double angle formula, sin(2θ) = 2sin(θ)cos(θ).
Correct Answer: A — 2sin(θ)cos(θ)
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Q. What is the value of sin(30°) + cos(60°)?
Solution
sin(30°) = 1/2 and cos(60°) = 1/2. Therefore, sin(30°) + cos(60°) = 1/2 + 1/2 = 1.
Correct Answer: A — 1
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Q. What is the value of sin(45°) + cos(45°)?
Solution
sin(45°) = cos(45°) = √2/2. Therefore, sin(45°) + cos(45°) = √2/2 + √2/2 = √2.
Correct Answer: A — √2
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Q. What is the value of sin(90° - A)?
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A.
cos A
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B.
sin A
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C.
tan A
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D.
sec A
Solution
Using the co-function identity, sin(90° - A) = cos A.
Correct Answer: A — cos A
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Q. What is the value of sin(90° - x)?
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A.
cos(x)
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B.
sin(x)
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C.
tan(x)
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D.
sec(x)
Solution
Using the co-function identity, sin(90° - x) = cos(x).
Correct Answer: A — cos(x)
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Q. What is the value of sin(90°)?
Q. What is the value of sin^2(x) + cos^2(x)?
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A.
1
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B.
0
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C.
sin(x)
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D.
cos(x)
Solution
By the Pythagorean identity, sin^2(x) + cos^2(x) = 1 for all x.
Correct Answer: A — 1
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Q. What is the value of sin^2(θ) + cos^2(θ)?
-
A.
1
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B.
0
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C.
sin(θ)
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D.
cos(θ)
Solution
By the Pythagorean identity, sin^2(θ) + cos^2(θ) = 1.
Correct Answer: A — 1
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Q. What is the value of tan(30°)?
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A.
√3/3
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B.
1/√3
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C.
√3
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D.
3
Solution
tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.
Correct Answer: A — √3/3
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Q. What is the value of tan(45° + x)?
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A.
tan x
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B.
1 + tan x
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C.
(1 - tan x)/(1 + tan x)
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D.
1 - tan x
Solution
Using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B), we have tan(45° + x) = (1 + tan x) / (1 - 1*tan x) = (1 + tan x).
Correct Answer: B — 1 + tan x
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Q. Which of the following is an identity?
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A.
sin^2 x + cos^2 x = 1
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B.
tan x = sin x / cos x
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C.
sec x = 1/cos x
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D.
All of the above
Solution
All the given options are trigonometric identities.
Correct Answer: D — All of the above
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Q. Which of the following is the correct identity for sin(2A)?
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A.
2sinAcosA
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B.
sin^2A + cos^2A
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C.
sinA + cosA
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D.
sinAcosA
Solution
The double angle formula states that sin(2A) = 2sinAcosA.
Correct Answer: A — 2sinAcosA
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Q. Which of the following is true for all angles A?
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A.
sin^2 A + cos^2 A = 1
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B.
tan A = sin A/cos A
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C.
sec A = 1/cos A
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D.
All of the above
Solution
All the given identities are true for all angles A.
Correct Answer: D — All of the above
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