Trigonometric Ratios for Competitive Exam Success

Trigonometric Ratios

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

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

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

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?

A. 30
B. 60
C. 90
D. 45

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

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

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°

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

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?

A. 1/2
B. 1
C. √3/2
D. 0

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°)?

A. 0
B. 1/2
C. √3/2
D. 1

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

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

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?

A. 1
B. √2
C. 2
D. 1/2

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

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

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

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

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

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

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

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°?

A. 2
B. 1/2
C. √3
D. 1

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

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°)?

A. 1
B. √3
C. √2
D. 0

Solution

tan(60°) = √3.

Correct Answer: B — √3

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Trigonometric Ratios MCQ & Objective Questions

Understanding Trigonometric Ratios is crucial for students preparing for school and competitive exams in India. These ratios form the foundation of trigonometry, which is a significant part of mathematics curricula. Practicing MCQs and objective questions on Trigonometric Ratios not only enhances conceptual clarity but also boosts confidence, helping students score better in their exams.

What You Will Practise Here

Definition and significance of Trigonometric Ratios
Key formulas for sine, cosine, and tangent ratios
Understanding reciprocal ratios: cosecant, secant, and cotangent
Applications of Trigonometric Ratios in real-life problems
Graphical representation of Trigonometric functions
Solving problems using Trigonometric Ratios in right-angled triangles
Identifying and using Trigonometric identities

Exam Relevance

Trigonometric Ratios are frequently tested in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to apply these ratios in various contexts, including problem-solving and theoretical explanations. Common question patterns include direct calculations, application-based scenarios, and conceptual understanding, making it essential to master this topic for effective exam preparation.

Common Mistakes Students Make

Confusing the definitions of different Trigonometric Ratios
Misapplying the formulas in complex problems
Overlooking the importance of angle measurement (degrees vs. radians)
Neglecting to simplify answers when required
Failing to recognize the relationships between different Trigonometric Ratios

FAQs

Question: What are the primary Trigonometric Ratios?
Answer: The primary Trigonometric Ratios are sine, cosine, and tangent.

Question: How can I effectively prepare for Trigonometric Ratios questions?
Answer: Regular practice of MCQs and understanding the underlying concepts will greatly enhance your preparation.

Question: Are Trigonometric Ratios important for competitive exams?
Answer: Yes, they are crucial as they frequently appear in various competitive exams like NEET and JEE.

Now is the time to strengthen your understanding of Trigonometric Ratios! Dive into our practice MCQs and test your knowledge to excel in your exams.

Trigonometric Ratios

Trigonometric Ratios MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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