CAT Trigonometry Questions 2025: Download PDF with Questions & Answers

Overview: The CAT exam's Quantitative Aptitude section can sometimes include questions testing your knowledge of trigonometry. This blog post equips you with the tools to navigate these CAT Trigonometry Questions effectively. Continue reading to get the top questions here!

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• 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, CAT trigonometry syllabus to ace your score on the CAT exam in 2025!

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CAT Trigonometry Questions 2025

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

• 0
• 10
• 11
• 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?

• 35 m
• 50 m
• 58 m
• 73.2 m

Answer: 73.2 m

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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

• 4
• 3
• 6
• 1

Answer: 3

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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?

• 1: root3
• root 3
• 1:1
• 1:3

Answer: 1:3

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

• 5
• 2
• 3
• -5

Answer: -5

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

• 13
• 12
• 15
• 10

Answer: 13

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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:

• w/sinα(1+cos2α)
• w/sin2αcosα
• w/cosα(1+sin2α)
• 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?

• 5√3/2
• 5√3
• Both A and B
• Can’t be determined

Answer: Both 1 and 2

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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?

• 74
• 23
• 13
• 20

Answer: 23

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

• 1/t
• t
• √t Sec x
• t/Sinx

Answer: t

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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?

• 3√3 m
• 1.5√3 m
• 2/√3 m
• 6/√3 m

Answer: 1.5√3 m

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

• 2√mn
• 4√mn
• m – n
• 2mn

Answer: 4√mn

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Tips to Solve CAT Trigonometry Questions 2025

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 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.

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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.

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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 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 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.

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Important Formulas For CAT Trigonometry Questions 2025

• 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 trigonometry might not be the most frequent topic on the CAT, mastering it can 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

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