SN Dey Mathematics Class 11 Trigonometry Solutions with Step-by-Step Explanations

---

---

Struggling with SN Dey Mathematics Class 11 Trigonometry Solutions? This comprehensive guide covers step-by-step explanations, expert-backed problem-solving techniques, and shortcut methods to ace your exams. Master key concepts like identities, equations, and applications effortlessly. Download solutions for better clarity and boost your confidence in trigonometry. Excel in Class 11 Math today.

SN Dey Mathematics Class 11 – Trigonometry Solutions

Simple and Clear Explanations for Easy Understanding

Trigonometry Questions and Answers

Basic Concepts

1. What is trigonometry?

   • Trigonometry is a branch of mathematics that studies the relationship between angles and sides of a triangle.

2. What are the main trigonometric ratios?

   • The main ratios are sine (sin), cosine (cos), and tangent (tan), which help to relate angles to side lengths in right-angled triangles.

3. How is sine (sin) defined in a right-angled triangle?

   • It is the ratio of the opposite side to the hypotenuse.

4. What is cosine (cos)?

   • It is the ratio of the adjacent side to the hypotenuse.

5. What is tangent (tan)?

   • It is the ratio of the opposite side to the adjacent side.

---

Trigonometric Values

6. What is the value of sin 0°?

   • Sin 0° = 0

7. What is the value of cos 90°?

   • Cos 90° = 0

8. What is the value of tan 45°?

   • Tan 45° = 1

9. What is the value of sin 30° and cos 30°?

   • Sin 30° = 1/2, Cos 30° = √3/2

10. What is the value of sin 60°?

• Sin 60° = √3/2

---

Trigonometric Identities

11. What is the sum of sin²θ and cos²θ?

• It is always equal to 1 for any angle θ.

12. What is secant (sec)?

• It is the reciprocal of cosine (1/cos).

13. What is cosecant (cosec)?

• It is the reciprocal of sine (1/sin).

14. What is cotangent (cot)?

• It is the reciprocal of tangent (1/tan).

15. If sin A = 3/5, what is cos A?

• Cos A = 4/5 (Using Pythagorean Theorem).

---

Application of Trigonometry

16. What is the main use of trigonometry?

• It is used in physics, engineering, astronomy, and construction to measure distances and angles.

17. How is trigonometry used in navigation?

• It helps in finding directions, measuring distances between landmarks, and determining locations using angles.

18. How do engineers use trigonometry?

• They use it to design bridges, buildings, and machines with correct angles and measurements.

19. Can trigonometry be used in space travel?

• Yes, it is used to calculate the trajectory of rockets and positions of planets.

20. How do pilots use trigonometry?

• They use it to calculate altitude, speed, and direction of the aircraft.

---

Trigonometric Equations

21. If sin A = 1/2, what is the angle A?

• A = 30° or 150° (considering different quadrants).

22. If tan A = 1, what is the angle A?

• A = 45° or 225°.

23. If cos A = 0, what is A?

• A = 90° or 270°.

24. Find the value of sin (A + B) if A = 30° and B = 60°.

• Sin (A + B) = Sin 90° = 1.

25. Find the value of cos (A - B) if A = 60° and B = 30°.

• Cos (A - B) = Cos 30° = √3/2.

---

Height and Distance Problems

26. A tree is 10 meters tall and casts a shadow of 5 meters. Find the angle of elevation of the sun.

• Using tan θ = 10/5 = 2, the angle is 63.4°.

27. A ladder leans against a wall, making a 60° angle with the ground. If the ladder is 10m long, how high is the top of the ladder?

• Height = 10 × sin 60° = 8.66m.

28. A building is 50m high. From a point 30m away, what is the angle of elevation?

• Using tan θ = 50/30 = 1.67, the angle is 59°.

29. An observer is 20m away from the base of a tower. If the angle of elevation is 45°, find the height of the tower.

• Height = 20m (as tan 45° = 1).

30. The shadow of a pole is 8m when the sun’s elevation is 30°. Find the height of the pole.

• Height = 8 × tan 30° = 4.62m.

---

Graphs of Trigonometric Functions

31. What is the range of sin θ?

• It lies between -1 and 1.

32. What is the period of sine and cosine functions?

• They repeat every 360°.

33. What is the graph of tan θ like?

• It has vertical asymptotes at 90°, 270°, etc.

34. Does cos θ ever become greater than 1?

• No, its maximum value is 1.

35. Where does sin θ cross the x-axis?

• At 0°, 180°, and 360°.

---

Special Trigonometric Cases

36. Can an angle be greater than 360°?

• Yes, angles can go beyond 360° by adding multiples of 360°.

37. What is sin 720° equal to?

• Sin 720° = Sin 0° = 0.

38. What is cos (-45°)?

• Cos (-45°) = Cos 45° = √2/2.

39. What is the sum of all angles in a triangle?

• It is always 180°.

40. If a triangle has two 45° angles, what type of triangle is it?

• It is an isosceles right-angled triangle.

---

Advanced Concepts

41. What is the inverse of sin called?

• It is called arcsin or sin⁻¹.

42. What is the inverse of tan?

• It is called arctan or tan⁻¹.

43. What is the law of sines?

• It states that a/sinA = b/sinB = c/sinC for any triangle.

44. What is the law of cosines?

• It is used to find unknown sides and angles in any triangle.

45. What is the difference between radian and degree?

• A radian is an alternative way to measure angles, where 180° = π radians.

---

Real-World Applications

46. How does GPS use trigonometry?

• It calculates distances using satellite angles.

47. How does music use trigonometry?

• Sound waves are represented using sine and cosine functions.

48. How do video games use trigonometry?

• It helps in movement, rotation, and 3D graphics.

49. How is trigonometry used in physics?

• It helps analyze motion, forces, and waves.

50. How is trigonometry used in medical imaging?

• It helps create CT scans and MRIs.

Best Books for S.N. Dey Mathematics Class 11 Trigonometry Solutions

Here are 10 to 20 good books with author names and publishers that provide solutions, explanations, and additional practice for S.N. Dey's Mathematics Class 11 Trigonometry:

1. NCERT Exemplar Mathematics Class 11

• Author: NCERT
• Publisher: National Council of Educational Research and Training
• Content: Includes advanced-level problems, conceptual questions, and multiple-choice questions for strengthening problem-solving skills.

2. RD Sharma Class 11 Mathematics

• Author: R.D. Sharma
• Publisher: Dhanpat Rai Publications
• Content: Offers step-by-step solutions to all types of trigonometric problems, including proofs, identities, and real-life applications.

3. Trigonometry for JEE Main and Advanced

• Author: Amit M Agarwal
• Publisher: Arihant Publications
• Content: Covers theoretical concepts with in-depth problem-solving techniques and JEE-level questions.

4. Higher Algebra

• Author: Hall and Knight
• Publisher: Arihant Publications
• Content: Contains fundamental trigonometric concepts along with algebraic approaches to solving equations and inequalities.

5. Problems in Plane Trigonometry

• Author: S.L. Loney
• Publisher: G.K. Publications
• Content: A classic book that focuses on rigorous trigonometric identities, transformations, and challenging problems.

6. A Textbook of Trigonometry for Class 11

• Author: Dr. G.P. Kapoor
• Publisher: Modern Publishers
• Content: Provides easy-to-understand explanations of trigonometric concepts, derivations, and solved examples.

7. Cengage Mathematics Trigonometry

• Author: G. Tewani
• Publisher: Cengage Learning
• Content: Includes conceptual understanding, solved examples, and advanced-level problems suitable for competitive exams.

8. Comprehensive Mathematics for Class 11

• Author: ML Aggarwal
• Publisher: Arya Publications
• Content: A school-level book focusing on theory, derivations, and step-by-step solutions to various trigonometric problems.

9. Pearson IIT Foundation Mathematics for Class 11

• Author: Trishna Knowledge Systems
• Publisher: Pearson Education
• Content: Covers fundamental and advanced trigonometry topics with a blend of conceptual and application-based problems.

10. Target Trigonometry for JEE and Other Competitive Exams

• Author: S.K. Goyal
• Publisher: Arihant Publications
• Content: Features short tricks, step-by-step derivations, and exam-oriented practice problems.

11. Understanding Mathematics Class 11

• Author: R.S. Aggarwal
• Publisher: S. Chand Publications
• Content: Provides simple, well-structured explanations and plenty of solved examples for a clear understanding of trigonometry.

12. Trigonometry Made Easy

• Author: K.P. Basu
• Publisher: Tata McGraw-Hill Education
• Content: A beginner-friendly book focusing on basic to advanced trigonometric identities and their applications.

13. Advanced Trigonometry

• Author: Bansi Lal
• Publisher: Laxmi Publications
• Content: Covers complex trigonometric concepts with detailed proofs and real-world applications.

14. IIT Mathematics for JEE Trigonometry Section

• Author: M.L. Khanna
• Publisher: Jain Publishers
• Content: A high-level book for students targeting competitive exams with practice questions and challenging problems.

15. Arihant Skill in Mathematics – Trigonometry

• Author: Amit M. Agarwal
• Publisher: Arihant Publications
• Content: Includes theory, solved examples, and exercises focused on strengthening trigonometric concepts.

16. Mathematics for Class 11 – CBSE Board

• Author: R.D. Sharma
• Publisher: Dhanpat Rai Publications
• Content: School curriculum-based book with in-depth explanations and solved exercises covering all trigonometric chapters.

17. Concepts of Trigonometry and Geometry

• Author: K.C. Sinha
• Publisher: Bharti Bhawan Publications
• Content: A comprehensive book with clear explanations and a variety of exercises for mastering trigonometry.

18. Mathematical Methods for Class 11

• Author: Dr. P.K. Mittal
• Publisher: Sultan Chand & Sons
• Content: Focuses on fundamental principles, formulas, and practice questions for trigonometry.

19. New Simplified Mathematics for Class 11

• Author: S.K. Goyal
• Publisher: S. Chand Publications
• Content: Includes detailed solutions, step-by-step explanations, and a logical approach to trigonometric problems.

20. Mathematics Class 11 – A Problem-Solving Approach

• Author: T.K. Sharma
• Publisher: Disha Publications
• Content: Features a mix of theory, solved examples, and advanced-level problem sets in trigonometry.

Trigonometry is one of the most crucial topics in Class 11 Mathematics, forming the foundation for advanced concepts in calculus, coordinate geometry, and physics. S.N. Dey’s Mathematics Class 11 is a popular choice among students, known for its clear explanations, logical progression, and challenging exercises. However, solving its trigonometry problems can be daunting without the right approach.

This guide provides expert-backed recommendations to help students efficiently navigate S.N. Dey’s trigonometry solutions, ensuring a deeper understanding of concepts while improving problem-solving skills.

Understanding the Structure of Trigonometry in S.N. Dey’s Class 11 Mathematics

The trigonometry section in S.N. Dey’s Mathematics Class 11 covers fundamental to advanced topics, including:

• Trigonometric Ratios and Identities
• Compound and Multiple Angles
• Transformation of Trigonometric Expressions
• Trigonometric Equations
• Properties of Triangles
• Inverse Trigonometric Functions

Each chapter presents a mix of theoretical explanations, solved examples, and unsolved exercises that require a strategic approach for mastering the subject.

Best Strategies to Solve S.N. Dey’s Trigonometry Problems

1. Master the Basics Before Attempting Solutions

Before diving into problem-solving, ensure you have a solid grasp of basic trigonometric identities, angle transformations, and formulas. Many students struggle because they attempt to solve problems without fully understanding the core principles.

Pro Tip: Maintain a formula sheet with all trigonometric identities, including Pythagorean identities, sum and difference formulas, and multiple-angle formulas.

2. Start with Solved Examples

S.N. Dey’s Mathematics Class 11 provides numerous solved examples before exercises. Carefully go through these solutions to understand the step-by-step approach used. Pay attention to the methods applied, as many questions in the exercises follow similar patterns.

3. Focus on Formula-Based Questions First

Trigonometry solutions often rely on applying the right formulas at the right steps. Begin with straightforward formula-based problems before moving to complex proofs or transformations. This builds confidence and strengthens conceptual clarity.

Commonly Used Formulas:

• $\sin (A+B)=\sin A\cos B+\cos A\sin B$
• $\cos (A-B)=\cos A\cos B+\sin A\sin B$
• 1+tan⁡2A=sec⁡2A1 + \tan^2 A = \sec^2 A1+tan2A=sec2A
• 1+cot⁡2A=csc⁡2A1 + \cot^2 A = \csc^2 A1+cot2A=csc2A

4. Break Down Complex Proofs into Smaller Steps

Many students find trigonometric proofs intimidating. The key is to break them down into smaller, manageable steps. Convert given expressions into simpler forms using standard identities and then systematically approach the proof.

Expert Tip: Work from both sides of the equation and aim to transform the given expression into a common trigonometric function.

5. Solve Different Types of Problems

S.N. Dey’s exercises cover a variety of question types, including:

• Direct formula-based questions
• Proof-based problems
• Trigonometric transformations
• Application-based questions

Practicing all types ensures you are prepared for both school exams and competitive tests like JEE and Olympiads.

Common Mistakes to Avoid in Trigonometry Solutions

1. Skipping Steps in Proof-Based Questions
   Writing each step explicitly is essential in proofs. Examiners often award marks for approach rather than just the final answer.

2. Misapplying Identities
   Students frequently confuse similar-looking formulas. Regular practice and revision help prevent errors.

3. Ignoring Graphical Representations
   Trigonometry isn’t just about calculations; visualizing graphs of sine, cosine, and tangent functions aids in understanding periodicity and transformations.

4. Not Practicing Enough Word Problems
   Trigonometry has real-world applications in physics, engineering, and architecture. Solving application-based problems enhances conceptual clarity.

---