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title: "Trigonometric Functions"
board: "CBSE"
curriculum: "CBSE"
class: "Class 11"
subject: "Mathematics"
book: "Mathematics"
chapter: "Trigonometric Functions"
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# Trigonometric Functions
The chapter provides an introduction to trigonometry, a branch of mathematics derived from the Greek words 'trigon' and 'metron', which means 'measuring the sides of a triangle'. Initially developed to address geometric problems, trigonometry finds applications in navigation, surveying, engineering, and various scientific fields today.

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## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Trigonometric Functions |
| Pages | 43-75 |

---

## Chapter Summary

### Short Summary
This chapter focuses on the generalization of trigonometric ratios to trigonometric functions and explores their properties, as well as introducing the measurement of angles.

### Detailed Summary
The chapter begins by discussing the origins of trigonometry and its historical significance in solving geometric problems. It highlights the applications of trigonometry in contemporary fields. Key concepts introduced include the definition and measurement of angles, along with the transition from trigonometric ratios to functions. The chapter encompasses angle measurement in degrees and radians, essential for further study in trigonometry.

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## Topic-Wise Explanation

### Introduction
Trigonometry is defined as the measurement of the sides of a triangle, and it has historical roots in various professions requiring navigation and mapping.

### Angles
An angle is defined by the rotation of a ray about its initial point, with the initial and terminal sides, as well as the vertex identified. Angles can be quantified using different units, primarily degrees and radians. Positive angles denote counterclockwise rotation, while negative angles indicate clockwise rotation.

### Trigonometric Functions
This section expands on the concept of trigonometric functions derived from the basic ratios studied in earlier classes, necessary for solving a variety of mathematical problems.

### Trigonometric Functions of Sum and Difference of Two Angles
This section appears to be omitted in the context provided.

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## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Trigonometry as Measurement | Trigonometry measures the sides of triangles and applies to navigation and engineering. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Angle | A measure of rotation around a point, quantified in degrees or radians. |
| Radian | A unit of angle measurement based on the radius of a circle. |

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## Important Points for Revision

* Trigonometry is rooted in the measurement of triangles.
* The term derives from Greek origins.
* Trigonometric functions generalize earlier studied ratios.
* A measure of an angle is the rotation from the initial to the terminal side.
* Positive angles rotate counterclockwise; negative angles rotate clockwise.
* Two primary measurement units for angles are degrees and radians.
* Trigonometric functions have extensive applications in various scientific fields.
* Understanding angles is crucial for advanced mathematical concepts.

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## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Trigonometry | The study of measuring the sides of triangles. |
| Angle | The figure formed by two rays sharing a common endpoint. |

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## Practice Questions

### Short Answer Questions
1. What is the origin of the word 'trigonometry'?
2. How did sea captains historically use trigonometry?
3. What characterizes a positive angle?
4. Define a radian.
5. What are the two most common units for measuring angles?

### Long Answer Questions
1. Explain the significance of studying trigonometric functions compared to trigonometric ratios.
2. Describe how angles are measured and the importance of each measurement system.
3. Discuss the various applications of trigonometry in real-world scenarios.

---

## Related Concepts
* Trigonometric Ratios
* Angle Measurement
* Applications of Trigonometry

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 66f15931e361cd99fe370d28 |
| Canonical URL | https://www.edzy.ai/cbse-class-11-mathematics-trigonometric-functions |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-11-mathematics-trigonometric-functions.md |