Trigonometri Jumlah Dan Selisih Sudut
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Diketahui sudut A dan sudut B adalah sudut lancip. Jika cos A = 4/5 dan cos B = 24/25. Tentukanlah nilai cos(a+B) ?
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1/5
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2/5
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3/5
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4/5
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Explore the intriguing world of trigonometry in angles and their relationships. This quiz assesses your understanding of sum and difference identities, focusing on acute angles and their cosine and sine values, enhancing your analytical skills in mathematical concepts.
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Jika 0 < A < π, memenuhi A+B = (2/3)π dan sin A = 2sin B, maka tentukanlah (A – B) ?
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π/3
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π/2
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π
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2π/3
Correct Answer
A. π/2Explanation
The given equation states that A + B = (2/3)π and sin A = 2sin B. We need to find the value of (A - B). From the given equation, we can rearrange it as sin A = 2sin (π - A) since sin (π - A) = sin A. This implies that A = π - A, which means A = π/2. Therefore, (A - B) = π/2 - B. Since we don't have any information about B, we cannot determine its value. Hence, the given answer of π/2 is correct.Rate this question:
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- 3.
Diketahui sudut lancip A dengan cos 2A = 1/3. Nilai sin A =…
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1/3 (V3)
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2/3 (V3)
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V3
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2V3
Correct Answer
A. 1/3 (V3)Explanation
The given equation cos 2A = 1/3 can be rewritten as 2cos^2(A) - 1 = 1/3. Simplifying further, we have 2cos^2(A) = 4/3. Dividing both sides by 2, we get cos^2(A) = 2/3. Taking the square root of both sides, we have cos(A) = √(2/3). Since sin^2(A) + cos^2(A) = 1, we can substitute the value of cos(A) in this equation to find sin(A). Therefore, sin(A) = √(1 - 2/3) = √(1/3) = 1/√(3) = 1/3√(3). Hence, the answer is 1/3 (V3).Rate this question:
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- 4.
Pada suatu segitiga siku-siku ABC berlaku cos A cos B = ½ , maka cos (A-B) sama dengan….
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-1
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-1/2
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1/2
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1
Correct Answer
A. 1Explanation
In a right triangle ABC, if cos A cos B = 1/2, then cos (A-B) = 1.Rate this question:
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- 5.
Jika tan x = a , maka sin 2x sama dengan…
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2a / (a2+ 1)
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A / (a2+ 1)
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2a / (a2-1)
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A / (a2- 1)
Correct Answer
A. 2a / (a2+ 1)Explanation
The given question is asking for the value of sin 2x if tan x = a. To find this, we can use the identity sin 2x = 2sin x cos x. Since tan x = a, we can rewrite it as sin x / cos x = a. Solving for sin x, we get sin x = a cos x. Substituting this into the identity, sin 2x = 2(a cos x)(cos x) = 2a cos^2 x. Since cos^2 x = 1 - sin^2 x, we can rewrite it as sin 2x = 2a(1 - sin^2 x) = 2a - 2a sin^2 x. Dividing both sides by 1 - sin^2 x (which is equal to cos^2 x), we get sin 2x = 2a / (1/cos^2 x) = 2a / (a^2 + 1). Therefore, the correct answer is 2a / (a^2 + 1).Rate this question:
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Current Version
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Mar 20, 2023Quiz Edited by
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Jan 26, 2017Quiz Created by
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