NPAT Trigonometry Questions and Answers

Overview: The NPAT exam focuses on applying formulas in practical problems rather than lengthy derivations. A good grasp of NPAT trigonometry questions ensures speed and accuracy in the quantitative section.

Trigonometry questions in the NMIMS NPAT exam can seem tricky at first, but it doesn't have to be.

Most students struggle not because the questions are hard, but because they try to memorize formulas without understanding how to use them.

In NPAT trigonometry questions are usually straightforward: they test your conceptual understanding and problem-solving skills.

If you know the key formulas, can visualize triangles, and follow a step-by-step approach, you can solve these questions quickly and accurately.

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Understanding the Role of Trigonometry in NPAT 2026

Trigonometry forms a crucial component of the quantitative section in NPAT.

Questions are designed to test your understanding of basic concepts and your ability to apply formulas under time constraints.

Unlike traditional board exams, NPAT exam emphasizes problem-solving speed and logical application rather than long derivations.

Key concepts that frequently appear NPAT trigonometry questions:

• Trigonometric Ratios: Sine, Cosine, Tangent, and their reciprocals (Cosecant, Secant, Cotangent).
• Trigonometric Identities: Pythagorean identities, reciprocal identities, and quotient identities.
• Heights and Distances: Application of trigonometric ratios to solve real-world problems.
• Angles of Elevation and Depression: Classic NPAT questions often involve these concepts.
• Trigonometric Equations: Simple equations solvable using standard identities.

NPAT Trigonometry Sample Questions with Answers

Let's take a look at some of the NPAT trigonometry questions:

Q1. If sin θ = 3/5, find cos θ.

A) 4/5

B) 2/5

C) 5/3

D) 3/4

Answer: A) 4/5

Q2. If tan θ = 1, then θ is:

A) 30°

B) 45°

C) 60°

D) 90°

Answer: B) 45°

Q3. Simplify: 1 + tan² θ

A) sin² θ

B) cos² θ

C) sec² θ

D) csc² θ

Answer: C) sec² θ

Q4. The angle of elevation of the top of a tower from a point 30 m away from its base is 45°. FindA) 30 m

B) 45 m

C) 60 m

D) 15 m

Answer: A) 30 m

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Q5. If sin θ = 5/13, find tan θ.

A) 12/5

B) 5/12

C) 13/12

D) 12/13

Answer: B) 5/12

Q6. Solve for θ: 2 sin θ - 1 = 0

A) 30°

B) 45°

C) 60°

D) 90°

Answer: A) 30°

Q7. If cot θ = 3/4, find csc θ.

A) 5/3

B) 5/4

C) 4/5

D) 3/5

Answer: A) 5/3

Q8. The angle of depression of a car from the top of a 50 m tall building is 30°. Find the distance

A) 50√3 m

B) 100 m

C) 50 m

D) 25√3 m

Answer: A) 50√3 m

Q9. If sin A = 12/13 and cos B = 4/5, find sin A cos B + cos A sin B.

A) 56/65

B) 33/65

C) 60/65

D) 1/2

Answer: A) 56/65

Q10. Find the value of cos² θ - sin² θ if cos θ = 3/5.

A) 7/25

B) 4/5

C) 3/5

D) 3/25

Answer: A) 7/25

Q11. If tan θ = 7/24, find sin θ.

A) 7/25

B) 7/25

C) 24/25

D) 24/7

Answer: A) 7/25

Q12. A ladder leans against a wall such that it makes an angle of 60° with the ground. If the foot A) 10 m

B) 5 m

C) 5√3 m

D) 10√3 m

Answer: C) 5√3 m

Q13. If sin θ = 0.6, then cos θ is:

A) 0.8

B) 0.6

C) 0.4

D) 0.5

Answer: A) 0.8

Q14. Solve for θ: cos 2θ = 1/2

A) 30°, 150°

B) 60°, 120°

C) 45°, 135°

D) 90°, 180°

Answer: A) 30°, 150°

Q15. If the shadow of a pole 12 m high is 6 m long, find the angle of elevation of the sun.

A) 30°

B) 45°

C) 60°

D) 90°

Answer: C) 60°

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Common Types of Trigonometry Questions in NPAT

NPAT trigonometry questions can be broadly categorized into four main types.

Understanding each type and how to approach it is key to scoring well.

1. Direct Ratio-Based Questions

What they test:

Basic trigonometric ratios – sine, cosine, and tangent.

Example:

Find sin θ, cos θ, or tan θ for a given right-angled triangle.

Tips to solve:

• Identify the opposite, adjacent, and hypotenuse sides.
• Use fundamental formulas:
  • sin θ = Opposite / Hypotenuse
  • cos θ = Adjacent / Hypotenuse
  • tan θ = Opposite / Adjacent
• Draw a triangle for clarity.

2. Identity-Based Problems

What they test:

Simplifying expressions using trigonometric identities.

Example:

Simplify 1 + tan²θ or sin²θ + cos²θ.

Tips to solve:

• Memorize key identities (Pythagorean, reciprocal, quotient).
• Replace expressions with equivalent identities to simplify.

3. Word Problems (Heights and Distances)

What they test:

Application of trigonometry to real-life scenarios.

Examples:

• Finding the height of a tower using an angle of elevation.
• Calculating distances between two points using triangles.

Tips to solve:

• Draw the scenario and label known values.
• Choose the correct trigonometric ratio for the given angle.
• Check units and rounding.

4. Equation Solving

What they test:

Solving basic trigonometric equations for θ.

Examples:

• 2 sin θ – 1 = 0
• cos²θ – sin²θ = 0

Tips to solve:

• Isolate the trigonometric function first.
• Use standard angle values (0°, 30°, 45°, 60°, 90°).
• Consider all possible solutions in the given range (usually 0°–360°).

Practical Strategies to Tackle NPAT Trigonometry Questions

1. Master the Basics: First A solid understanding of ratios, identities, and their relationships is crucial. Memorize key formulas-they save precious time in exams.
2. Visualize with Diagrams: Drawing triangles and labeling sides and angles helps reduce calculation errors and makes word problems easier to solve.
3. Use Simplification Techniques: NPAT questions are designed to be solved quickly. Look for patterns and simplify expressions using standard trigonometric identities.
4. Practice Past NPAT Questions: Reviewing previous years' NPAT papers provides insight into commonly tested topics and question formats.
5. Time Management: Trigonometry problems, especially word problems, can be time-consuming. Practice solving questions in a timed setting to enhance speed and accuracy.

Recommended Resources

• NCERT Class 11 and 12 Mathematics: Ideal for understanding foundational concepts.
• NPAT Previous Year Question Papers: Helps in identifying frequently asked trigonometry questions.
• Online Mock Tests and Quizzes: Great for time-bound practice and instant feedback.
• Selecting the right NPAT books is crucial for efficient preparation for the NPAT exam.
   

With these strategies, you can approach NPAT trigonometry questions with precision, speed, and a clear mind-ensuring you maximize your score in the quantitative section.

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Key Takeaways

• Focus on Conceptual Understanding: Grasping the basics is essential to solve NPAT trigonometry questions efficiently.
• Practice Strategically: Solving past questions and sample problems helps build familiarity and speed.
• Use Visuals and Simplifications: Drawing diagrams and simplifying expressions reduces errors and saves time.