Trigonometry Quiz: Angle Addition And Subtraction

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Quizzes Created: 1110 | Total Attempts: 2,473,266

Questions: 10 | Attempts: 192 | Updated: Aug 16, 2023

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Trigonometry Quiz: Angle Addition And Subtraction - Quiz

Trigonometry is one of the most studied branches of mathematics. Are you ready for a trigonometry quiz? We have one here for you. As we all know, trigonometry is known as a math branch that focuses on the study of relationships between side lengths as well as angles of triangles. This quiz has angle addition and subtraction questions and answers for your practice. Let's see how well you perform with them. All the best.

Questions and Answers

1.

Cos 105° =
- A.
  
  (√2 - √6)/4
- B.
  
  (√2 + √6)/4
- C.
  
  (√2 + √5)/4
- D.
  
  (√3 + √6)/4
Correct Answer
B. (√2 + √6)/4

Explanation
The correct answer is (√2 + √6)/4. This can be determined by using the cosine function and the unit circle. The cosine of 105 degrees can be found by evaluating the x-coordinate of the point on the unit circle corresponding to 105 degrees. By using the values of √2 and √6, which are the x-coordinates of the points on the unit circle corresponding to 45 degrees and 60 degrees respectively, we can add them together and divide by 4 to get the cosine of 105 degrees.

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1
0
2.

Sin B = -5/13, where π<A<3π/2 ,B =
- A.
  
  -14/13
- B.
  
  -14/12
- C.
  
  -12/13
- D.
  
  -11/13
Correct Answer
C. -12/13

Explanation
In the given question, it is stated that sin B = -5/13. Since the range of A is π

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3.

________ = SinA.CosB - CosA.SinB
- A.
  
  Sin (A -B)
- B.
  
  Sin (A +B)
- C.
  
  Cos (A -B)
- D.
  
  None of these
Correct Answer
A. Sin (A -B)

Explanation
The given expression, SinA.CosB - CosA.SinB, can be simplified using the trigonometric identity for the sine of the difference of two angles, which is Sin (A - B). Therefore, the correct answer is Sin (A - B).

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4.

If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B,Then A =
- A.
  
  45 degree
- B.
  
  48 degree
- C.
  
  50 degree
- D.
  
  55 degree
Correct Answer
A. 45 degree

Explanation
The given information states that tan(A + B) = √3 and tan(A – B) = 1/√3. Since tan(A + B) = √3, we can conclude that the angle (A + B) must be 60 degrees, as the tangent of 60 degrees is √3. Similarly, tan(A – B) = 1/√3 implies that the angle (A – B) must be 30 degrees, as the tangent of 30 degrees is 1/√3.

Now, we can solve for A by adding the two equations: (A + B) + (A – B) = 60 + 30. This simplifies to 2A = 90, and dividing both sides by 2 gives A = 45 degrees. Therefore, the correct answer is 45 degrees.

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5.

If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B,Then B =
- A.
  
  10 degree
- B.
  
  12 degree
- C.
  
  15 degree
- D.
  
  20 degree
Correct Answer
C. 15 degree

Explanation
The given information states that tan(A + B) = √3 and tan(A – B) = 1/√3. Since the values of tan(A + B) and tan(A – B) are known, we can use the trigonometric identities to find the value of B. By using the identity tan(A + B) = (tanA + tanB) / (1 - tanA * tanB), we can substitute the given values to get (√3) = (tanA + tanB) / (1 - tanA * tanB). Similarly, using the identity tan(A – B) = (tanA - tanB) / (1 + tanA * tanB), we can substitute the given values to get (1/√3) = (tanA - tanB) / (1 + tanA * tanB). By solving these two equations simultaneously, we can find the value of B, which is 15 degrees.

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6.

Given cos A = -4/5, where π/2<A<π, A =
- A.
  
  4/5
- B.
  
  3/5
- C.
  
  2/3
- D.
  
  -2/3
Correct Answer
B. 3/5

Explanation
The given information states that cos A is equal to -4/5, where A is an angle between π/2 and π. Since cosine is equal to the adjacent side divided by the hypotenuse in a right triangle, we can conclude that the adjacent side is -4 and the hypotenuse is 5. By using the Pythagorean theorem, we can find the opposite side, which is 3. Therefore, the sine of A is equal to 3/5.

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7.

If sin 3A = cos (A – 26°), where 3A is an acute angle,A =
- A.
  
  29 degree
- B.
  
  31 degree
- C.
  
  43 degree
- D.
  
  77 degree
Correct Answer
A. 29 degree

Explanation
The given equation sin 3A = cos (A – 26°) implies that the sine of 3A is equal to the cosine of (A – 26°). Since the sine and cosine functions have a phase difference of 90°, we can conclude that 3A and (A – 26°) must also have a phase difference of 90°. This means that 3A and (A – 26°) are complementary angles. Since A is an acute angle, the only possible value for A that satisfies this condition is 29 degrees.

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8.

(√6 - √2)/4 =
- A.
  
  Sin 20 degree
- B.
  
  Sin 55 degree
- C.
  
  Sin 12 degree
- D.
  
  Sin 15 degree
Correct Answer
D. Sin 15 degree

Explanation
To solve the given equation (√6 - √2)/4, we can simplify it by rationalizing the denominator. We multiply both the numerator and the denominator by the conjugate of the denominator, which is (√6 + √2). This results in (√6 - √2)(√6 + √2) = (√6)^2 - (√2)^2 = 6 - 2 = 4. Therefore, the simplified equation becomes 4/4, which simplifies further to 1. The value of sin 15 degrees is also 1/4. Hence, the answer is sin 15 degrees.

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9.

Cos (A+B) =
- A.
  
  SinA.CosB - CosA.SinB
- B.
  
  CosA.CosB - SinA.SinB
- C.
  
  SinA.CosB + CosA.SinB
- D.
  
  None of these
Correct Answer
B. CosA.CosB - SinA.SinB

Explanation
The given expression, CosA.CosB - SinA.SinB, is the correct answer because it represents the formula for the cosine of the sum of two angles. The formula states that the cosine of the sum of angles A and B is equal to the product of the cosines of each angle minus the product of the sines of each angle. Therefore, the correct answer is CosA.CosB - SinA.SinB.

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10.

A = -4/5, where π/2<A<π ,Tan A =
- A.
  
  5/4
- B.
  
  -3/6
- C.
  
  -3/5
- D.
  
  -3/4
Correct Answer
D. -3/4

Explanation
The given information states that A is an angle between π/2 and π, and that Tan A is equal to -4/5. The only option that satisfies this condition is -3/4.

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Current Version
Aug 16, 2023

Quiz Edited by
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Oct 28, 2022

Quiz Created by
Keith Foster

Trigonometry Quiz: Angle Addition And Subtraction

Cos 105° =

Sin B = -5/13, where π<A<3π/2 ,B =

________ = SinA.CosB - CosA.SinB

If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B,Then A =

If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B,Then B =

Given cos A = -4/5, where π/2<A<π, A =

If sin 3A = cos (A – 26°), where 3A is an acute angle,A =

(√6 - √2)/4 =

Cos (A+B) =

A = -4/5, where π/2<A<π ,Tan A =