NCERT Class 11 Mathematics Mathematics: Chapter 3 — TRIGONOMETRIC FUNCTIONS
This chapter, Trigonometric Functions, introduces the generalization of trigonometric ratios to trigonometric functions and explores their properties. It begins by defining an angle as a measure of rotation, distinguishing between positive (anticlockwise) and negative (clockwise) rotations. The chapter discusses two primary units for measuring angles: degree measure and radian measure. Degree measure defines an angle based on fractions of a complete revolution, with a degree divided into minutes and seconds (1° = 60', 1' = 60"). The text also touches upon the historical origins and diverse applications of trigonometry, from ancient geometry and navigation to modern seismology and atomic physics. This foundational understanding is crucial for further study in mathematics and related scientific fields within the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 3 — TRIGONOMETRIC FUNCTIONS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 470 |
Learning outcomes
- Understand the concept of an angle as a measure of rotation.
- Differentiate between positive and negative angles.
- Learn about the degree measure of an angle and its subdivisions (minutes and seconds).
- Recognize the historical development and wide-ranging applications of trigonometry.
- Generalize trigonometric ratios to trigonometric functions.
Vocabulary
| Word | Meaning |
|---|---|
| Trigonometry | The branch of mathematics dealing with the relations between the sides and angles of triangles. |
| Angle | A measure of rotation of a ray about its initial point. |
| Initial side | The original ray in the definition of an angle. |
| Terminal side | The final position of the ray after rotation. |
| Vertex | The point of rotation of the initial ray. |
| Degree measure | A unit of angle measurement where one complete revolution is 360 degrees. |
| Minute | One sixtieth of a degree (1° = 60'). |
| Second | One sixtieth of a minute (1' = 60"). |
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Practice questions
- What is the origin of the word 'trigonometry'? Answer: The word 'trigonometry' is derived from the Greek words 'trigon' (triangle) and 'metron' (measure), meaning 'measuring the sides of a triangle'.
- Define an angle in terms of rotation. Answer: An angle is defined as the measure of rotation of a given ray about its initial point.
- When is an angle considered positive and when negative? Answer: An angle is positive if the rotation is anticlockwise and negative if the rotation is clockwise.
- How is a degree divided into smaller units? Answer: A degree is divided into 60 minutes (1° = 60'), and a minute is divided into 60 seconds (1' = 60").
Practice MCQs
Q1. The word 'trigonometry' comes from which language?
Explanation: The term 'trigonometry' is derived from Greek words 'trigon' and 'metron'.
Q2. In the definition of an angle, the point of rotation is called the:
Explanation: The point from which the rotation originates is defined as the vertex of the angle.
Q3. An anticlockwise rotation of a ray results in a:
Explanation: By convention, anticlockwise rotation is considered positive.
Q4. How many minutes are there in one degree?
Explanation: One degree is divided into 60 minutes, denoted as 1° = 60'.
Q5. Which of the following is NOT a historical application of trigonometry mentioned?
Explanation: While trigonometry is used in engineering, architecture is not explicitly mentioned as a historical application in this section.
Frequently asked questions
What is trigonometry?
Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles, and it has applications in many fields.
How is an angle measured?
Angles can be measured in degrees or radians. This chapter focuses on degree measure, where a full revolution is 360 degrees.
What are the components of an angle?
An angle consists of an initial side, a terminal side, and a vertex, which is the point of rotation.
What is the difference between a positive and a negative angle?
A positive angle is formed by anticlockwise rotation, while a negative angle is formed by clockwise rotation.
How are degrees further divided?
A degree is divided into 60 minutes (1° = 60'), and each minute is divided into 60 seconds (1' = 60").
Where is trigonometry used?
Trigonometry is used in navigation, surveying, seismology, designing circuits, describing atomic states, predicting tides, and analyzing musical tones, among other areas.
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NCERT Class 11 Mathematics — Mathematics — Chapter 3 — TRIGONOMETRIC FUNCTIONS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.