NCERT Solutions Class 10 Maths Chapter 8 guides you through Introduction to Trigonometry with step-by-step solutions across 3 exercises covering 19 questions. You’ll learn how to calculate trigonometric ratios (sin, cos, tan) for different angles, apply fundamental trigonometric identities like sin²θ + cos²θ = 1, and solve problems involving complementary angles. These solutions show you exactly how to simplify expressions, prove identities, and find missing values—essential skills for coordinate geometry, heights and distances, and higher mathematics.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry – Complete Guide
NCERT Class 10 Chapter 8 – Introduction to Trigonometry opens the door to one of mathematics’ most powerful tools. You will explore the six trigonometric ratios and understand how they relate the angles and sides of right-angled triangles. This chapter carries significant weight in your CBSE board exam with approximately 6 marks, making it a high-priority topic that demands thorough understanding and consistent practice.
📊 CBSE Class 10 Maths Chapter 8 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Trigonometry |
| Difficulty Level | Hard |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You’ll begin by learning the definitions of sine, cosine, tangent, cosecant, secant, and cotangent ratios, and discover how to calculate them for angles like 0°, 30°, 45°, 60°, and 90°. The chapter then introduces you to fundamental trigonometric identities, particularly sin²θ + cos²θ = 1 and its variations, which form the backbone of solving complex problems. These identities appear frequently in both objective MCQs and subjective questions worth 2-3 marks each.
Trigonometry isn’t just theoretical—it has real-world applications in navigation, architecture, physics, and engineering. Understanding how angles and distances relate helps in calculating heights of buildings, distances of ships from shore, and angles of elevation or depression. These practical applications make trigonometry essential for competitive exams and higher studies in science and mathematics.
Quick Facts – Class 10 Chapter 8
| 📖 Chapter Number | Chapter 8 |
| 📚 Chapter Name | Introduction to Trigonometry |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 19 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Expect a mix of question types: 1-mark MCQs testing basic ratios and values, 2-mark problems on applying identities, and 3-mark questions combining multiple concepts. This chapter also connects seamlessly with Chapter 9 (Applications of Trigonometry) and serves as foundation for Class 11 mathematics. Master the standard angle values, practice identity-based problems regularly, and you’ll find this chapter becomes one of your strongest scoring areas in the CBSE board examination.
NCERT Solutions Class 10 Maths Chapter 8 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 8.1 | Complete step-by-step solutions for 11 questions | 📥 Download PDF |
| Exercise 8.2 | Complete step-by-step solutions for 4 questions | 📥 Download PDF |
| Exercise 8.3 | Complete step-by-step solutions for 4 questions | 📥 Download PDF |
Introduction to Trigonometry – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Pythagorean Theorem \(a^2 + b^2 = c^2\) | Relates sides of a right-angled triangle (a, b are legs, c is hypotenuse) Note: Make sure ‘c’ is always the hypotenuse (the side opposite the right angle). | Finding a missing side of a right triangle when you know the other two sides. Crucial for defining trigonometric ratios. |
| Sine (sin θ) \(\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}\) | Ratio of the side opposite to the angle θ to the hypotenuse. Note: SOH (Sine = Opposite / Hypotenuse). Remember to check if your calculator is in degree mode. | Finding the side opposite to an angle when you know the angle and hypotenuse, or finding the angle when you know the opposite side and hypotenuse. |
| Cosine (cos θ) \(\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}\) | Ratio of the side adjacent to the angle θ to the hypotenuse. Note: CAH (Cosine = Adjacent / Hypotenuse). Adjacent side is the side next to the angle (not the hypotenuse). | Finding the side adjacent to an angle when you know the angle and hypotenuse, or finding the angle when you know the adjacent side and hypotenuse. |
| Tangent (tan θ) \(\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}\) | Ratio of the side opposite to the angle θ to the side adjacent to the angle θ. Note: TOA (Tangent = Opposite / Adjacent). Also, tan θ = sin θ / cos θ | Finding the side opposite to an angle when you know the angle and adjacent side, or finding the angle when you know the opposite and adjacent sides. |
| Cosecant (cosec θ) \(\csc \theta = \frac{1}{\sin \theta} = \frac{\text{Hypotenuse}}{\text{Opposite}}\) | Reciprocal of sine θ. Note: cosec θ is not the reciprocal of cos θ. It’s the reciprocal of sin θ. | When you know sin θ and need cosec θ, or when you need to relate hypotenuse and opposite side. |
| Secant (sec θ) \(\sec \theta = \frac{1}{\cos \theta} = \frac{\text{Hypotenuse}}{\text{Adjacent}}\) | Reciprocal of cosine θ. Note: sec θ is not the reciprocal of sin θ. It’s the reciprocal of cos θ. | When you know cos θ and need sec θ, or when you need to relate hypotenuse and adjacent side. |
| Cotangent (cot θ) \(\cot \theta = \frac{1}{\tan \theta} = \frac{\text{Adjacent}}{\text{Opposite}}\) | Reciprocal of tangent θ. Note: cot θ = cos θ / sin θ. Remember it’s the reciprocal of tan θ. | When you know tan θ and need cot θ, or when you need to relate adjacent and opposite sides. |
| tan θ in terms of sin and cos \(\tan \theta = \frac{\sin \theta}{\cos \theta}\) | Expressing tan θ using sin θ and cos θ. Note: Useful in proving trigonometric identities. | When you know sin θ and cos θ and need to find tan θ. |
| cot θ in terms of sin and cos \(\cot \theta = \frac{\cos \theta}{\sin \theta}\) | Expressing cot θ using cos θ and sin θ. Note: Useful in proving trigonometric identities. | When you know cos θ and sin θ and need to find cot θ. |
| Trigonometric Identity 1 \(\sin^2 \theta + \cos^2 \theta = 1\) | Fundamental trigonometric identity. Note: sin² θ means (sin θ)². This is the most important identity; learn it well. | Simplifying trigonometric expressions, proving identities, and finding sin θ if you know cos θ (or vice versa). |
| Trigonometric Identity 2 \(1 + \tan^2 \theta = \sec^2 \theta\) | Another important trigonometric identity. Note: Can be rearranged as sec² θ – tan² θ = 1 or tan² θ = sec² θ – 1. | Simplifying expressions involving tan θ and sec θ, proving identities. |
| Trigonometric Identity 3 \(1 + \cot^2 \theta = \csc^2 \theta\) | Trigonometric identity involving cot θ and csc θ. Note: Can be rearranged as csc² θ – cot² θ = 1 or cot² θ = csc² θ – 1. | Simplifying expressions involving cot θ and csc θ, proving identities. |
| sin(90° – θ) \(\sin (90^\circ – \theta) = \cos \theta\) | Sine of the complementary angle. Note: Remember to use degrees, not radians. | Simplifying expressions involving complementary angles. Converting sin to cos and vice versa. |
| cos(90° – θ) \(\cos (90^\circ – \theta) = \sin \theta\) | Cosine of the complementary angle. Note: Remember to use degrees, not radians. | Simplifying expressions involving complementary angles. Converting cos to sin and vice versa. |
| tan(90° – θ) \(\tan (90^\circ – \theta) = \cot \theta\) | Tangent of the complementary angle. Note: Remember to use degrees, not radians. | Simplifying expressions involving complementary angles. Converting tan to cot and vice versa. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 8
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