---
type: "Chapter"
knowledge_type: "chapter"
entity_type: "chapter"
id: "69f869c0293c3123114dab4e"
title: "Introduction to Trigonometry"
board: "CBSE"
curriculum: "CBSE"
class: "Class 10"
subject: "Mathematics"
book: "Mathematics"
chapter: "Introduction to Trigonometry"
chapter_slug: "introduction-to-trigonometry"
canonical_url: "https://www.edzy.ai/cbse-class-10-mathematics-introduction-to-trigonometry"
markdown_url: "https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-introduction-to-trigonometry.md"
source_type: "examSubjectBookChapter"
source_id: "69f869c0293c3123114dab4e"
source_pdf: "https://edzy-ai.s3.ap-south-1.amazonaws.com/edzy-express-ts/5f6b6319-dc3d-471a-970d-9349fae4d6d2.pdf"
source: "Edzy"
version: 1
last_updated: "2026-06-22"
---

# Introduction to Trigonometry
Trigonometry occupies a central position in mathematics and deals with the relationships between the angles and sides of triangles, particularly right triangles. The word "trigonometry" comes from the Greek words for three, sides, and measure. Historically, it played a crucial role in fields such as astronomy and continues to be essential in modern engineering and physical sciences.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Introduction to Trigonometry |
| Pages | 113-132 |

---

## Chapter Summary

### Short Summary
This chapter introduces trigonometric ratios, which relate the angles and sides of right triangles, and explores specific angles such as 0°, 30°, 45°, 60°, and 90°.

### Detailed Summary
The chapter begins by discussing real-life situations where right triangles can be formed and their relevance to measuring distances and heights. It defines trigonometric ratios including sine, cosine, tangent, cosecant, secant, and cotangent. The historical context provided illustrates the evolution of terminology in trigonometry from ancient practices to modern applications. The chapter includes methods to derive these ratios from specific triangles and their relationships, as well as identities involving these ratios. Lastly, it presents the values of trigonometric ratios for angles 0°, 30°, 45°, 60°, and 90°.

---

## Topic-Wise Explanation

### Trigonometric Ratios
Trigonometric ratios for an acute angle in a right triangle are defined as follows:
- Sine: $\sin A = \frac{\	ext{opposite}}{\	ext{hypotenuse}}$
- Cosine: $\cos A = \frac{\	ext{adjacent}}{\	ext{hypotenuse}}$
- Tangent: $	an A = \frac{\	ext{opposite}}{\	ext{adjacent}}$
- Cosecant: $\csc A = \frac{1}{\sin A}$
- Secant: $\sec A = \frac{1}{\cos A}$
- Cotangent: $\cot A = \frac{1}{\	an A}$
These ratios help in understanding the relationships within right triangles and can be derived from one another:
- $	an A = \frac{\sin A}{\cos A}$.

### Trigonometric Ratios of Some Specific Angles
The values of trigonometric ratios for specific angles are:
- For $30^\circ$: $\sin 30^\circ = \frac{1}{2}, \cos 30^\circ = \frac{\sqrt{3}}{2}, \	an 30^\circ = \frac{1}{\sqrt{3}}$.
- For $45^\circ$: $\sin 45^\circ = \frac{1}{\sqrt{2}}, \cos 45^\circ = \frac{1}{\sqrt{2}}, \	an 45^\circ = 1$.
- For $60^\circ$: $\sin 60^\circ = \frac{\sqrt{3}}{2}, \cos 60^\circ = \frac{1}{2}, \	an 60^\circ = \sqrt{3}$.
- For $0^\circ$: $\sin 0^\circ = 0, \cos 0^\circ = 1$.
- For $90^\circ$: $\sin 90^\circ = 1, \cos 90^\circ = 0$.

### Summary
The chapter encapsulates the fundamental principles of trigonometry, establishing a foundation for understanding the behavior of angles and sides in right triangles, alongside historic developments in the terminology and application of trigonometric functions.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Trigonometric Ratios | Relationships of sides and angles in right triangles. |
| Applications of Trigonometry | Used in various fields like astronomy, engineering, and physical sciences. |

---

## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Sine | Ratio of the opposite side to the hypotenuse in a right triangle. |
| Cosine | Ratio of the adjacent side to the hypotenuse in a right triangle. |
| Tangent | Ratio of the opposite side to the adjacent side in a right triangle. |
| Cosecant | Reciprocal of sine. |
| Secant | Reciprocal of cosine. |
| Cotangent | Reciprocal of tangent. |

---

## Important Points for Revision
* Trigonometry deals with angles and sides of triangles.
* Key trigonometric ratios are sine, cosine, and tangent.
* Trigonometric ratios vary based on the angle but not on the triangle's size.
* Specific angles have predefined trigonometric ratio values.
* The terminology used today has historical roots tracing back to ancient mathematicians.

---

## Practice Questions
### Short Answer Questions
1. Define sine of an angle in a right triangle.
2. What is the relationship between sine and cosecant?
3. Calculate $\sin 30^\circ$.
4. What is $	an 45^\circ$?
5. If $\cos A = \frac{3}{5}$, what is $\sin^2 A + \cos^2 A$?

### Long Answer Questions
1. Prove that if $\sin B = \sin Q$, then $\angle B = \angle Q$.
2. Given that $	an A = \frac{4}{3}$, calculate all other trigonometric ratios of angle A.
3. Explain how to derive the values of trigonometric ratios for angles $30^\circ$ and $60^\circ$ using geometry.

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69f869c0293c3123114dab4e |
| Canonical URL | https://www.edzy.ai/cbse-class-10-mathematics-introduction-to-trigonometry |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-introduction-to-trigonometry.md |