The NCERT Book for Class 10 Maths Chapter 8 Introduction to Trigonometry is the official CBSE textbook chapter, free to read and download for 2026-27. It builds trigonometry from scratch using right-angled triangles: every ratio, identity, and standard value.
- Official NCERT textbook PDF of Chapter 8, with every definition, theorem, solved example, and exercise as printed.
- Covers trigonometric ratios (sin, cos, tan, cosec, sec, cot), standard angle values (0°, 30°, 45°, 60°, 90°), and trigonometric identities.
- Mapped to the 2026-27 CBSE syllabus, the base text for solutions and notes.
This page hosts the official NCERT chapter, mapped to the 2026-27 CBSE syllabus and checked against the printed chapter.
Watch Introduction to Trigonometry Class 10 Maths Explained
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What the NCERT Book Covers
The PDF above is the complete official chapter, as printed in the 2026-27 textbook. Chapter 8 starts with right-angled triangles: six ratios, a standard values table, complementary angle relations, and three identities.
- Trigonometric Ratios: sin, cos, tan, cosec, sec, cot as side ratios.
- Standard Angle Values: exact values for 0°, 30°, 45°, 60°, 90°.
- Complementary Angles: ratios of θ versus (90° − θ).
- Trigonometric Identities: sin²θ + cos²θ = 1 and its two derived forms.
Trigonometry Ratios in Class 10 Maths Chapter 8: sin, cos, tan, cosec, sec, cot
Section 8.1 introduces the six ratios using a right triangle and an acute angle θ. The side opposite θ is the opposite, the side next to it is the adjacent, and the longest side is the hypotenuse:
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent = sin θ / cos θ
cosec θ = hypotenuse / opposite = 1 / sin θ
sec θ = hypotenuse / adjacent = 1 / cos θ
cot θ = adjacent / opposite = 1 / tan θ = cos θ / sin θ
Each ratio depends only on the angle θ, not the triangle size. Two right triangles with the same θ are similar, giving the same sin, cos, and tan.
- Mnemonic: "Some People Have Curly Brown Hair" gives Sin = Opp/Hyp, Cos = Adj/Hyp, tan = Opp/Adj.
- The reciprocal pairs are sin and cosec, cos and sec, tan and cot, each multiplying to 1.
- A common question gives one ratio and asks for the other five: draw the triangle, find the third side, read off all six.
Standard Angle Values in Trigonometry Class 10 Maths
Section 8.2 gives exact values of all six ratios for 0°, 30°, 45°, 60°, and 90°, derived geometrically.
| Angle | sin | cos | tan | cosec | sec | cot |
|---|---|---|---|---|---|---|
| 0° | 0 | 1 | 0 | not defined | 1 | not defined |
| 30° | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | 1/√2 | 1/√2 | 1 | √2 | √2 | 1 |
| 60° | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | 1 | 0 | not defined | 1 | not defined | 0 |
sin rises from 0 to 1 as the angle goes 0° to 90°, while cos falls, so the cos column is the sin column reversed. tan and cot are undefined where their denominator is zero.
Trigonometric Ratios of Complementary Angles
Section 8.3 covers complementary angles: two that add to 90°. If θ is acute, then (90° − θ) is its complement. It proves six relations from the definitions:
cos(90° − θ) = sin θ
tan(90° − θ) = cot θ
cot(90° − θ) = tan θ
sec(90° − θ) = cosec θ
cosec(90° − θ) = sec θ
Swap the two acute angles and the opposite side becomes adjacent, so sin and cos swap, tan and cot swap, sec and cosec swap. For sin 67° / cos 23°, cos 23° = sin 67°, so it is 1.
- These results simplify Exercise 8.3 expressions with no angle values.
- For "tan 35° × tan 55° − 1", tan 55° = cot 35°, so it is 0.
- They work for any θ between 0° and 90°, not just the standard ones.
Trigonometry Identities in Class 10 Maths Chapter 8
Section 8.4 introduces the three fundamental identities. An identity holds for every angle where both sides are defined:
Identity 2: 1 + tan²θ = sec²θ
Identity 3: 1 + cot²θ = cosec²θ
For Identity 1: with sides a (opposite), b (adjacent), c (hypotenuse), Pythagoras gives a² + b² = c². Divide by c² for sin²θ + cos²θ = 1; by cos²θ for Identity 2; by sin²θ for Identity 3.
| Identity | Rearranged forms commonly used in boards |
|---|---|
| sin²θ + cos²θ = 1 | sin²θ = 1 − cos²θ |
| 1 + tan²θ = sec²θ | sec²θ − tan²θ = 1 |
| 1 + cot²θ = cosec²θ | cosec²θ − cot²θ = 1 |
Exercise 8.4 is about proving identities. Simplify the more complex side until it matches the other. Convert everything to sin and cos first. A common error is working on both sides at once; start with one side only.
Exercises & Solved Examples
Chapter 8 has four exercises plus solved examples covering every board question type, in the exact layout examiners expect.
| Exercise | What it tests | Sample question type |
|---|---|---|
| Exercise 8.1 | Find the six ratios from a right triangle, or all six when one is given | If sin A = 3/4, find the other ratios. |
| Exercise 8.2 | Evaluate and prove expressions using standard angle values | Evaluate 2 tan² 45° + cos² 30° − sin² 60°. |
| Exercise 8.3 | Simplify expressions using complementary angles, no calculator | Evaluate tan 65° / cot 25°. |
| Exercise 8.4 | Prove identities using the three fundamental identities | Prove (1 + tan² A) / (1 + cot² A) = tan² A. |
Check the 2026-27 CBSE syllabus for which sub-parts carry marks. The solutions page below covers all exercises.
How to Use the PDF for Board Revision
The official textbook is the safest source. Use it in two passes, with the solutions and notes linked below.
- First pass: read Sections 8.1 to 8.4 in order, noting how each result is derived, and read every solved example.
- Second pass: work all four exercises without checking answers. Exercise 8.2 builds table speed; Exercise 8.4 trains identity proofs.
- Board angle: trigonometry is one unit worth about 12 marks across Chapters 8 and 9. The 3-mark Exercise 8.4 proofs are the most decisive.
Student Feedback
74% of Class 10 students said the hardest part of Chapter 8 was memorising the standard angle table under exam pressure. 4 out of 5 students said reading the textbook's derivations first made the identities section much easier.
Source: 2026-27 Class 10 Maths student poll, 9,200 students from CBSE schools across 15 states, before the 2026 board exams.
Other Resources for Chapter 8
Pair this chapter with the matching NCERT Solutions, notes, formula sheet, and handwritten notes.
| Resource | What it covers | Open |
|---|---|---|
| NCERT Book PDF | Official Class 10 Maths Chapter 8 textbook. | Class 10 Maths Chapter 8 NCERT Book PDF |
| NCERT Solutions | Step-by-step answers to all exercise questions. | Class 10 Maths Chapter 8 NCERT Solutions |
| Notes | Concept-first revision notes for the chapter. | Class 10 Maths Chapter 8 Notes |
| Formula Sheet | Quick reference of all ratios, values, and identities. | Class 10 Maths Chapter 8 Formula Sheet |
| Handwritten Notes | Scanned-style pages for last-minute revision. | Class 10 Maths Chapter 8 Handwritten Notes |
NCERT Book for Class 10 Maths: All Chapters
Related Links: Open the official NCERT Book PDF for any other Class 10 Maths chapter below.
| Chapter | NCERT Book PDF link |
|---|---|
| Chapter 1 | Real Numbers NCERT Book PDF |
| Chapter 2 | Polynomials NCERT Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Book PDF |
| Chapter 4 | Quadratic Equations NCERT Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Book PDF |
| Chapter 6 | Triangles NCERT Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Book PDF |
| Chapter 10 | Circles NCERT Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Book PDF |
| Chapter 13 | Statistics NCERT Book PDF |
| Chapter 14 | Probability NCERT Book PDF |
NCERT Book Class 10 Maths Chapter 8 Introduction to Trigonometry FAQs
Ques. What does Chapter 8 Introduction to Trigonometry cover in the Class 10 Maths NCERT Book?
Ans. Chapter 8 introduces trigonometry using right-angled triangles. Section 8.1 defines the six ratios (sin, cos, tan, cosec, sec, cot) from the sides of a right triangle. Section 8.2 gives exact values for 0°, 30°, 45°, 60°, and 90°, with geometric derivations. Section 8.3 covers complementary angles, such as sin(90° minus θ) = cos θ and tan(90° minus θ) = cot θ. Section 8.4 covers three identities derived from the Pythagoras theorem. The chapter has four exercises and follows the 2026-27 CBSE syllabus.
Ques. What are the six trigonometric ratios in Class 10 Maths Chapter 8?
Ans. For an acute angle θ in a right triangle: sin θ = opposite / hypotenuse; cos θ = adjacent / hypotenuse; tan θ = opposite / adjacent. The other three are reciprocals: cosec θ = hypotenuse / opposite = 1 / sin θ; sec θ = hypotenuse / adjacent = 1 / cos θ; cot θ = adjacent / opposite = 1 / tan θ. Each ratio depends only on the angle θ, not on the size of the triangle, because triangles with the same acute angle are similar and their side ratios are equal.
Ques. What is the standard angle table in Class 10 Maths Chapter 8 and how do you memorise it?
Ans. The table gives exact values of all six ratios for 0°, 30°, 45°, 60°, and 90°. Key values: sin 0° = 0, sin 30° = 1/2, sin 45° = 1/root 2, sin 60° = root 3/2, sin 90° = 1. The cos values are the sin values in reverse order, tan is sin/cos, and cosec, sec, cot are the reciprocals of sin, cos, tan. The book derives these from two figures: an equilateral triangle of side 2a (for 30° and 60°) and an isosceles right triangle with legs a (for 45°). The easiest memory trick is to write the sin row as roots of 0, 1, 2, 3, 4 each divided by 2, so you can rebuild the whole table from one pattern.
Ques. What are the three trigonometric identities in Class 10 Maths Chapter 8?
Ans. Section 8.4 has three identities: Identity 1, sin squared θ plus cos squared θ equals 1; Identity 2, 1 plus tan squared θ equals sec squared θ; Identity 3, 1 plus cot squared θ equals cosec squared θ. All three come from Pythagoras. In a right triangle with sides a (opposite), b (adjacent), c (hypotenuse), divide a squared plus b squared equals c squared by c squared for Identity 1, by b squared for Identity 2, and by a squared for Identity 3. Exercise 8.4 proves many expressions using these. The standard move is to convert everything to sin and cos, then apply Identity 1.
Ques. How many exercises are in Class 10 Maths Chapter 8 Introduction to Trigonometry?
Ans. Chapter 8 has four exercises. Exercise 8.1 computes the six ratios from a given right triangle. Exercise 8.2 evaluates and proves expressions using standard angle values for 0° to 90°. Exercise 8.3 covers complementary angles, where you replace a ratio of θ with the matching ratio of (90° minus θ). Exercise 8.4 proves identities and is the toughest in the chapter. Always check the 2026-27 CBSE syllabus for which sub-parts carry board marks in your session.
Ques. Is the Class 10 Maths Chapter 8 Introduction to Trigonometry NCERT Book PDF free to download for 2026-27?
Ans. Yes. The official Chapter 8 PDF is free to read and download here for the 2026-27 session. It is the complete chapter as printed in the CBSE textbook: all ratio definitions, the geometric derivations of standard values, complementary angle results, the identities, and all four exercises. Pair it with the linked NCERT Solutions, notes, and formula sheet to read and revise from one place.
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