Trigonometric Ratios Formulas and Solved Examples in Right Triangles
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 and Basic Trigonometric Concepts
1. What is trigonometry in Maths?
Trigonometry is the branch of mathematics that studies the relationship between the angles and sides of triangles, especially right-angled triangles. It mainly deals with six trigonometric ratios:
- sin θ (sine)
- cos θ (cosine)
- tan θ (tangent)
- cosec θ
- sec θ
- cot θ
2. What are the six trigonometric ratios?
The six trigonometric ratios are sin θ, cos θ, tan θ, cosec θ, sec θ, and cot θ. In a right-angled triangle:
- sin θ = Opposite / Hypotenuse
- cos θ = Adjacent / Hypotenuse
- tan θ = Opposite / Adjacent
- cosec θ = 1 / sin θ
- sec θ = 1 / cos θ
- cot θ = 1 / tan θ
3. How do you find sin, cos, and tan of an angle?
You find sin θ, cos θ, and tan θ using the side lengths of a right-angled triangle. Follow these steps:
- Identify the opposite, adjacent, and hypotenuse sides.
- Apply the formulas:
- sin θ = Opposite / Hypotenuse
- cos θ = Adjacent / Hypotenuse
- tan θ = Opposite / Adjacent
4. What is a right-angled triangle in trigonometry?
A right-angled triangle is a triangle that has one angle equal to 90°. In trigonometry:
- The longest side is the hypotenuse.
- The side opposite the given angle is the opposite side.
- The side next to the angle (not hypotenuse) is the adjacent side.
5. What are the standard trigonometric values?
The standard trigonometric values are the exact values of sin, cos, and tan for common angles 0°, 30°, 45°, 60°, and 90°. Important values include:
- sin 30° = 1/2
- cos 60° = 1/2
- tan 45° = 1
- sin 90° = 1
- cos 0° = 1
6. What is the Pythagoras theorem in trigonometry?
The Pythagoras theorem states that in a right-angled triangle, Hypotenuse² = Opposite² + Adjacent². It is written as:
- c² = a² + b²
7. How do you solve a basic trigonometry problem?
You solve a basic trigonometry problem by identifying the known sides or angles and applying the correct trigonometric ratio. Steps:
- Draw and label the triangle.
- Choose the correct ratio (sin, cos, or tan).
- Substitute the known values.
- Solve algebraically.
8. What is the difference between sin and cos?
The difference between sin and cos lies in the sides they compare in a right triangle.
- sin θ = Opposite / Hypotenuse
- cos θ = Adjacent / Hypotenuse
9. Why is trigonometry important in real life?
Trigonometry is important because it helps calculate heights, distances, angles, and waves in real-world situations. Applications include:
- Engineering and construction
- Physics and astronomy
- Navigation and GPS systems
- Architecture and surveying
10. What are some common mistakes in trigonometry?
Common mistakes in trigonometry include using the wrong ratio or misidentifying triangle sides. Typical errors are:
- Confusing opposite and adjacent sides
- Forgetting to use degree or radian mode correctly
- Using incorrect standard values
- Not applying Pythagoras theorem properly
