An Overview Of The Introduction To Trigonometry Class 10
Trigonometry is the section of mathematics, which deals with the relationship between sides and angles of a triangle. Trigonometry exists because every straight-sided shapes can be broken down into triangles. Furthermore, it shares an intricate relationship with every branch of mathematics.
In this chapter of introduction to trigonometry, you will learn about the fundamental principles of it. Moreover, trigonometry primarily deals with right-angle triangles. In this chapter, you will learn how to find missing angles and sides of a triangle. Furthermore, the word ‘trigono’ means triangle and the word ‘metry’ means measurements.
Chapter 8 Introduction To Trigonometry
The introduction to trigonometry chapter has five sections, dealing with various aspect of trigonometry.
Section 8.1- Introduction
In this section, you will find a small overview along with various examples of trigonometry from your surroundings. For instance, if you are looking at the top of a post from a distance, can you find out its height without measuring it?
Real-life situations like these are calculated under this chapter trigonometry class 10.
The history of trigonometry can be traced back to ancient Egypt and Babylon.
Section 8.2- Trigonometric Ratios
In this part of class 10 chapter trigonometry you will learn about the various ratios of this section of mathematics. You will also learn about trigonometric functions like sine, cosine, etc. Additionally, there are detailed examples along with these explanations for your better understanding.
Furthermore, there is an exercise section, so that you can revise your learning to this point.
Section 8.3- Trigonometric Ratios of Specific Angles
This section of class 10th trigonometry chapter teaches you the ways to calculate trigonometric ratios of different angles. Moreover, you already know about 30°, 45°, 60°, and 90° from your previous geometry class. Additionally, you will also learn about the ratio of 0°.
Furthermore, here us a table comprising the trigonometric ratios of these angles.
Trigonometric Ratios of Specific Angles
Section 8.4- Trigonometric Ratios of Complementary Angels
As you already know that when the sum of two angles is equal to 90°, they are called complimentary angels. In this section of introduction to trigonometry ex 8.4, you will learn in-depth about the ratios associated with such angels.
Section 8.5- Trigonometric Identities
When the values of every variable involved in an equation are true, it is called an identity. Similarly, an equation of trigonometric ratios of an angle is called trigonometric identity, when it is valid for all values of the angles involved.
In this section of NCERT maths class 10 chapter trigonometry, you will learn about this topic in details.
Section 8.6- Summary
This section of CBSE class 10 maths introduction to trigonometry sums up all the points that you have studied in this chapter. This chapter ensures a revision of all the important topics.
Vedantu- Your Ideal Study Partner
Introduction to trigonometry is an essential chapter for class 10. Moreover, this chapter provides you with the basic knowledge of this section of mathematics. You learn about the fundamentals of trigonometry in this part. Additionally, you can visit the official website of Vedantu to access the important formulas and detailed solutions mentioned here.
Furthermore, if you are looking for expert guidance for trigonometry, you can download the Vedantu app and join the live classes. Additionally, you can access various study materials related to mathematics via this app.
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FAQs on Introduction to Trigonometry
1. What is trigonometry as introduced in the CBSE Class 10 Maths syllabus for 2025-26?
In Class 10, Introduction to Trigonometry is the branch of mathematics that studies the relationship between the angles and side lengths of a right-angled triangle. The core idea is that if you know some of the side lengths and angles of a right-angled triangle, you can find the others. This chapter lays the foundation by introducing trigonometric ratios, their values at specific angles, and fundamental identities.
2. What are the six basic trigonometric ratios for an acute angle in a right-angled triangle?
The six trigonometric ratios relate the acute angle 'A' to the ratios of the sides of a right-angled triangle (Opposite, Adjacent, Hypotenuse). They are:
- Sine (sin A) = Side Opposite to angle A / Hypotenuse
- Cosine (cos A) = Side Adjacent to angle A / Hypotenuse
- Tangent (tan A) = Side Opposite to angle A / Side Adjacent to angle A
- Cosecant (csc A) = 1 / sin A = Hypotenuse / Side Opposite to angle A
- Secant (sec A) = 1 / cos A = Hypotenuse / Side Adjacent to angle A
- Cotangent (cot A) = 1 / tan A = Side Adjacent to angle A / Side Opposite to angle A
3. How is trigonometry used to solve real-world problems?
Trigonometry has many practical applications where direct measurement is impossible. For example, it is used in:
- Astronomy to measure the distance to nearby stars.
- Geography and Navigation to determine locations and distances using GPS.
- Architecture and Engineering to calculate the height of buildings, bridges, and other structures without physically measuring them. For instance, if you know the distance to a building's base and the angle of elevation to its top, you can find its height using the tangent ratio.
- Video Game Development to control the movement and physics of characters and objects.
4. What is the most fundamental trigonometric identity in Class 10, and why is it important?
The most fundamental trigonometric identity for Class 10 is sin² A + cos² A = 1. This identity is crucial because it establishes a direct relationship between the sine and cosine of any angle. It is derived from the Pythagorean theorem in a right-angled triangle. Its importance lies in its ability to simplify complex trigonometric expressions and to find the value of one ratio if another is known, without needing to know the specific angle.
5. How are the trigonometric ratios of complementary angles related?
Complementary angles are two angles that add up to 90°. In trigonometry, there's a special relationship between the ratios of these angles. If 'A' is an acute angle, its complement is (90° - A). The relationships are:
- sin (90° – A) = cos A
- cos (90° – A) = sin A
- tan (90° – A) = cot A
- cot (90° – A) = tan A
- sec (90° – A) = csc A
- csc (90° – A) = sec A
This shows that the sine of an angle is the cosine of its complement, and so on, which simplifies many calculations.
6. Why is it necessary to memorise the trigonometric values for specific angles like 30°, 45°, and 60°?
Learning the trigonometric values for standard angles like 30°, 45°, and 60° is essential because they appear frequently in problems, not just in this chapter but in physics and higher mathematics as well. These values are derived from specific, easy-to-construct triangles (isosceles and equilateral). Knowing them allows for quick, exact calculations without a calculator, which is critical for solving problems efficiently during exams and for understanding the fundamental properties of these ratios.
7. What is the conceptual difference between sin A and the product sin × A?
This is a common point of confusion. sin A represents the 'sine of angle A'; it is a single term where 'sin' is the name of the function and 'A' is the input (the angle). It denotes the ratio of the opposite side to the hypotenuse for that specific angle. In contrast, sin × A would imply a multiplication between a quantity named 'sin' and a quantity named 'A'. The term 'sin' has no mathematical value on its own; it must operate on an angle. Therefore, sin A is a function, not a multiplication.
