12+ CAT Trigonometry Questions and Answers PDF Download Here [PYQs]

Overview: The CAT exam's Quantitative Aptitude section can sometimes include questions testing your knowledge of trigonometry. Read on to get the details on CAT Trigonometry Questions with Answers PDF effectively!

Download FREE CAT Trigonometry Questions PYQ

• The Common Admission Test (CAT) is an essential examination for students aspiring to pursue business and management careers at prestigious IIMs (Indian Institute of Management) and other leading business schools in India.
• Clearing the CAT entrance exam opens doors to IIMs and provides access to a robust alumni network, which can significantly contribute to career development.

Read on to learn the top CAT Trigonometry Questions pdfs for competitive exams pdf, CAT trigonometry syllabus to ace your score on the CAT exam in 2026!

What are CAT Trigonometry Questions 2026

CAT Trigonometry Questions PYQ usually involve the relationships between the angles and sides of triangles, focusing on sine, cosine, and tangent functions. They often appear as part of geometry problems, especially involving right-angled triangles.

While not heavily emphasized in the CAT syllabus, understanding basic trigonometric identities can help solve these questions quickly. Preparing for them ensures you don’t miss out on easy scoring opportunities.

Download CAT Trigonometry Question and Answers PDF

Important CAT Trigonometry Questions 2026 for Practice

Q1. Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], define the number of values that x can take.

A. 0
B. 10
C. 11
D. 21 

Answer: 21

Q2. A student is holding a banner at the top of a college building that is 100 meters high. When viewed from a point on the ground, the angle formed between the ground and the line of sight to the top of the student is 60°, and the angle formed between the ground and the line of sight to the top of the college building is 45°. What is the height of the student?

A. 35 m
B. 50 m
C. 58 m
D. 73.2 m

Answer: 73.2 m

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CAT Trigonometry questions pdf test your ability to handle mathematical problems related to angles, heights, distances, and trigonometric identities. These questions are not only conceptual but also involve logical reasoning, making them essential for a strong performance in the QA section.

Q3. If cos A + cos2 A = 1 and a sin12 A + b sin10 A + c sin8 A + d sin6 A - 1 = 0. Find the value of a+b/c+d

A. 4
B. 3
C. 6
D. 1

Answer: 3

Q4. In a regular hexagon TUVXYZ, there are towers at points U and X. The angle of elevation from point T to the top of the tower at U is 30 degrees, and to the top of the tower at X is 45 degrees. What is the ratio of the heights of the towers at U and X?

A. 1: root 3
B. root 3
C. 2:1
D. 1:3

Answer: 1:3

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Q5. The expression 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest possible value of ‘r’?

A. 5
B. 2
C. 3
D. -5

Answer: -5

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Q6. Find the maximum value of 3 cosx + 4 sinx + 8?

A. 13
B. 12
C. 15
D. 10

Answer: 13

Q7. In the figure below, the sheet of width W is folded along PQ so that R overlaps S. The length of PQ can be written as:

A. w/sinα(1+cos2α)
B. w/sin2αcosα
C. w/cosα(1+sin2α)
D. Any two of the above

Answer: Any of the above

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Q8. Ram and Shyam are positioned 10 km away from each other. They both observe a hot air balloon in the sky, each making angles of 60° and 30°, respectively. Determine the height at which the balloon is flying?

A. 5√3/2
B. 5√3
C. Both A and B
D. Can’t be determined

Answer: Both 1 and 2

Q9. In a right-angled triangle, the height is represented by 'p', the base by 'b', and the hypotenuse by 'h'. Considering that 'p' and 'b' are positive integers, which of the following values can the square of 'h' not represent?

A. 74
B. 23
C. 13
D. 20

Answer: 23

Q10. If 2Sinx/1+cosx+Sinx=t, 1–Cosx+Sinx/1+Sinx can be written as:

A. 1/t
B. t
C. √t Sec x
D. t/Sinx

Answer: t

Q11. A flag is flying on top of a building that is 7√3 meters tall. A person who is √3 meters tall, standing on the ground, sees the top and bottom of the flag pole at two angles of elevation that add up to 90 degrees. If the person is standing √135 meters away from the building, what is the height of the flag pole?

A. 3√3 m
B. 1.5√3 m
C. 2/√3 m
D. 6/√3 m

Answer: 1.5√3 m

Q12. tan ∅ + sin ∅ = m, tan ∅ - sin ∅ = n, Find the value of m2- n2

A. 2√mn
B. 4√mn
C. m – n
D. 2mn

Answer: 4√mn

Q13. 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

A. 5
B. -5
C. 4
D. 3

Answer: 5

Q14. Sin²⁰¹⁴x + Cos²⁰¹⁴x = 1, x in the range of [-5π, 5π], how many values can x take?

A. 15
B. 21
C. 24
D. 32

Answer: 21

Q15. Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

A. 1:√3
B. 1:2√3
C. 1:2
D. 3:4√3

Answer: 1:2√3

Q16. Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

A. 1:√3
B. 1:2√3
C. 1:2
D. 3:4√3

Answer: 1:2√3

Q17. Find the maximum and minimum value of 8 cos A + 15 sin A + 15

A. 11√2+15; 15
B. 30; 8
C. 32; -2
D. 23; 8

Answer: 32; -2

Q18. If cos A + cos² A = 1 and a sin¹² A + b sin¹⁰ A + c sin¹⁰ A + d sin⁶ A - 1 = 0. Find the value of a+b/c+d

A. 4
B. 3
C. 6
D. 1

Answer: 3

Q19. Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

A. 5√32
B. 5√3
C. Both A and B
D. Cannot be determined

Answer: Both A and B

Q20. Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

A. 20√3 minutes
B. 10 minutes
C. 10√3 minutes
D. 5 minutes

Answer: 10 minutes

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Tips to Solve CAT Trigonometry Questions 2026

Trigonometry plays a significant role in the Quantitative Aptitude section of the CAT entrance exam. Although the number of trigonometry CAT questions is typically limited, excelling in this area can provide a competitive advantage. Here are some strategies for tackling CAT trigonometry questions in CAT exam:

1. Establish a Strong Foundation

• Understanding the basics: It's important to have a solid grasp of sine, cosine, tangent, their co-functions, and their relationships with right-angled triangles.
• Mastering the formulas: Memorize the essential trigonometric formulas and their derived identities to reinforce your understanding of trigonometry CAT questions.

2. Refine Your Application Skills

• Practice with diverse angles: Don't limit yourself to special angles. Working with various angles can enhance your comfort level.
• Identify relevant formulas: Analyze each problem carefully to determine which trigonometric functions are most suitable.

3. Utilize Diagrams and Visualization

• Sketch diagrams: Visual representations of problems can aid in understanding the relationships between sides and angles in triangles.
• Label angles and sides: Mark known and unknown values on the diagram to keep track of the information.

4. Employ Smart Strategies

• Simplify before calculations: Try simplifying expressions using trigonometric identities before calculating.
• Consider estimation: If time is limited, use your understanding of trigonometric functions to make educated estimations.

5. Practice Regularly

• Solve past CAT papers: Familiarize yourself with trigonometry questions in CAT type and difficulty level by working through previous years' papers.
• Take mock tests: Regularly practice timed CAT mock tests to improve speed and accuracy.

Bonus Tip

• While memorizing formulas is important, strive to understand their underlying logic. Deepening comprehension can help you tackle CAT trigonometry questions pdf and solve non-standard problems.
• With dedicated practice and a strategic approach to CAT exam preparation, conquering trigonometry in the CAT exam and confidently tackling these questions on test day is achievable.

Important Formulas For CAT Trigonometry Questions 2026

• sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
• cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
• sin(a – b) = sin(a)cos(b) – cos(a)sin(b)
• cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
• tan(u+ v) = (tan(u) + tan(v))/ (1−tan(u) tan(v))
• tan(u- v) = (tan(u) − tan(v))/ (1+tan(u) tan(v))
• sin2Ꝋ + cos2Ꝋ = 1
• tan2Ꝋ + 1 = sec2Ꝋ
• cot2Ꝋ + 1 = cosec2Ꝋ
• sin 2θ = 2 sin θ cos θ
• cos 2θ = cos²θ – sin²θ
• tan 2θ = 2 tan θ / (1 – tan²θ)
• cot 2θ = (cot²θ – 1) / 2 cot θ

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Conclusion

While CAT trigonometry questions 2026 might not be among the most frequent topics in the CAT exam pattern, mastering them can still give you a significant advantage..

By solidifying your understanding of trigonometric functions and their formulas and applying strategic problem-solving techniques, you'll be well-equipped to tackle these CAT trigonometry questions confidently. Make it a point to practice CAT trigonometry previous year questions to familiarize yourself with the types of problems that have appeared in past exams.

Remember, consistent practice through solving past year papers and mock tests is critical to sharpening your skills and achieving success in the CAT.