Revision Notes For CBSE Class 10 Maths Chapter 8: Introduction To Trigonometry

Trigonometry is a mathematics branch that establishes relationships between the lengths of sides and angles of a triangle. It has wide applications in the field of oceanography, primarily. Moreover, there are other applications in real-life areas, such as music and other sound waves.

The inception of Trigonometry was because a computer cannot perceive musical sounds just as we do. However, it can represent the same in a Mathematical form as a function of sine or cosine, which can be developed into musical sounds. 

Therefore, not just in school, but you will need the basics of Trigonometry to build up your career too. For instance, a sound engineer needs the basics of this concept more. Hence, for a comprehensive study, our eminent faculties have drafted Class 10 Maths Chapter 8 Notes so that you can follow them before your upcoming CBSE board exam.

Students should know the fact that Trigonometry is based on a right-angled triangle. A right triangle has three sides: Height,  Base, and Hypotenuse.

Make sure you are aware of these three terms correctly before delving into the numerical of this chapter. Only after you have clarity on it will you be able to derive and represent the functions of Trigonometry. Hence, refer to our revision notes for compact study material to develop clarity on these. 

Diagrams presented alongside will help you to understand faster and more appropriately. Revising it before an exam will assist in recalling lessons more quickly and retaining information for longer. As a result, you can write your exams well and fetch better marks or grades.

Trigonometry Class 10 Notes – Revision Notes

Our Trigonometry Notes for Class 10 PDF are compiled by subject experts to help you get the most preferred revision notes. They have taught thousands of students in over a thousand cities, and thus they are aware of the complications students face in studying Trigonometry.

This is why they have incorporated shortcut techniques, and step-by-step calculations in Class 10 Maths Chapter 8 Notes. Revising from here will help you to develop a clear understanding of the same. Here is a brief overview of the chapter's content for your understanding.

CBSE 10 Maths Trigonometry Notes –Trigonometry ratios

Right from the beginning of this section, you will be made familiar with the trigonometric ratios, which are:

• Sine

• Cosine

• Tangent

• Cotangent

• Secant

• Cosecant 

Each of them is explained with the help of equations and diagrams to help you build a foundation of Trigonometry. Once you have built specific concepts from the grassroots, approaching the questions in the right direction during an exam becomes more comfortable.

So, ensure you follow our Class 10 Maths Chapter 8 Notes for convenience. Moreover, these files are available online, so you can download them and save in your devices for future reference.

Developing the concept of trigonometric ratios concerning the diagram is also essential as it will aid in solving numerical problems included in the latter part of the chapter. Therefore, build your concepts right in the beginning to solve the numerical quickly.

NCERT Class 10 Maths Notes PDF – Reciprocal Ratios

Once you have understood trigonometric ratios, you should also know about reciprocal ratios. These reciprocal ratios are the ratios of sine, cosine, and tangent functions. In our Notes for Class 10 Maths Trigonometry PDF, we have presented the ratios with corresponding equations and diagrams. 

Take a look at the expressions given in our revision notes, which are mentioned pointwise so that it is easier for you to recall the lessons faster before the exam. Refer to a right-angled triangle and determine the relevant functions.

Here, you should remember the reciprocals as given in our Class 10 Maths Chapter 8 Notes:

- 1/tan x = cot x

- 1/sin x = cosec x

- 1/cos x = sec x

Students must be thorough with the above three functions and be able to rearrange the same whenever needed. 

For instance, if 1/tan x = cot x, then tan x = 1/cot x.

Likewise, you should also be able to derive the other two functions. Also, the trigonometric identities need to be derived concerning a triangle.

Notes for Class 10 Maths – Trigonometric Identities

Under this section, you will learn a few advanced concepts related to trigonometric identities, commonly the functions' square terms. They are:

- Sin² A + cos² A = 1

- 1 + tan² A = sec² A

- 1 + cot² A = cosec² A

Three proofs are presented concerning these expressions. These three expressions have a vast list of applications in different forms, and you will find them, as you go through our Class 10 Maths Chapter 8 Notes. Further, students should be able to derive the required expressions from these using their logical reasoning skills.

You might not find any direct application of the same; however, you will have to use them in different forms by changing sides in expressing other equations. Usually, representing other equations using these forms simplifies the overall question. 

A simplified form thus helps in finding solutions faster. These tricks are available in our Introduction to Trigonometry Class 10 Notes PDF in the simplest ways to help you derive the other forms easily.

Revising these from our notes will also help you solve the sums faster in your board exams. Also, you can boost your exam scores when you solve the sums quicker and more accurately.

Class 10 Maths Chapter 8 Notes – Trigonometric Ratios of Standard Angles

In this section, you will be taught about some of the standard angles in trigonometry: 0⁰, 30⁰, 45⁰, 60⁰, and 90⁰. Students should know these fundamental angles as they are mostly used in numerical.

You will find a detailed explanation in our Class 10 Maths Chapter 8 Notes. It will help you understand and remember the formulas for longer. As a result, writing in exams will become more comfortable for you. Likewise, you can also score more in the exam too. 

A diagram is also presented alongside each degree which will further simplify your learning process. Another vital part you need to understand here is the Pythagoras theorem. Students are required to have clarity on this fundamental theorem to be able to solve advanced numerals, which are mainly based on this.

Make sure you know that Pythagoras' theorem is only applicable in the case of a right-angled triangle, which is why it is the only triangle used to determine trigonometric identities. To know more about this theorem and its properties, refer to our Introduction to Trigonometry Class 10 Notes. 

NCERT Class 10 Maths Notes PDF -  Line of sight

In this section, you will learn about advanced concepts related to Pythagoras' theorem. After dealing with straightforward numerals, you will have to solve word problems based on the same theorem. 

However, students find it often challenging to solve word problems related to Pythagoras theorem; however, on a closer look, you will find that it is not difficult as it seems in the first place. All it requires is logical and cognitive skills to approach a question. 

Go through our Class 10 Maths Chapter 8 Notes as it has the necessary shortcut tricks and details required to solve the word problems. You will know that:

• The angle of sight, as the term implies, is the angle formed when an imaginary line is drawn horizontally from the observer’s eye to the point where the object he is looking at.

• The imaginary line drawn from the eye to the object is called the line of sight.

• A pictorial representation of the same alongside the explanation is provided in our revision notes. 

• The diagram is well labeled for you to refer to it while studying. It will simplify the revision, and given that the human brain retains figures and diagrammatic information more than textual, it will help you remember the concept longer.

Make sure you understand this concept from our Class 10 Maths Chapter 8 Notes so that you can quickly solve the numerals problems in this chapter. It will also aid in solving the sums faster during exams. 

Class 10 Maths Chapter 8 Notes – Angle of Elevation

Similar to the line of sight, you will have to learn another term – angle of elevation. As the name implies, the angle is formed by the line of sight with the horizontal plane when the object is above it. It applies only if the observer is looking at an object located at a higher elevation than him.

For instance, a man standing on the ground and looking at the top of a tower or the moon could be used as examples for an understanding angle of elevation. A line diagram is provided to help you understand the topic easily. 

Refer to our Class 10 Maths Chapter 8 Notes for a compact representation of information. Before the exam, it is often difficult to go through the whole chapter and get hold of the critical topics at once. This is why we provide you with revision notes to make learning easier for you. 

Once these terms are clear, solving word problems will become a walk in the park for you. Our study materials are standard and updated as per the syllabus of upcoming board exams so that you can make the most of it by scoring higher in the exam.

Notes For Class 10 Maths – Angle of Depression

Just as an angle of elevation defines the angle when the observer is looking at an object present higher to him, the angle of depression is the opposite. Here, the observer is looking at something situated below the horizontal line.

These terms are equally important, and students should clearly understand the same before going for word problems. These terms are often confusing for students; however, you can refer to our Class 10 Maths Chapter 8 Notes to avoid confusion.

We have provided short tricks so that you can remember the concepts quickly and retain that for longer. Make sure you compare the observer with the horizontal line to determine whether it is an angle of elevation or depression when drawn from the eye of the observer. 

After drawing the lines, you will find that the overall picture forms a right-angled triangle. After that, you can use the trigonometric identities to determine the ratios. In an exam, you might be asked to calculate the height of the object or the observer, hence make sure you are thorough with the terms to solve accurately. 

Key Features of CBSE Class 10 Maths Chapter 8 Revision Notes

Go through the following points to know why our revision notes are mostly preferred by Class 10 students to prepare Maths Chapter 8 - Introduction To Trigonometry.

• We provide a detailed and accurate explanation of all the chapter topics covered in the Class 10 Maths NCERT textbooks.

• The notes we provide will be helpful for the CBSE board examinations, the Science Olympiads, and all other competitive exams.

• The subject experts use simple and readable language to help students understand the concepts easily.

• All the detailed explanations of topics are curated by our subject experts with a view to providing the most appropriate and authentic information to students after extensive research on every concept.

• Our Class 10 Maths Chapter 8 revision notes are free to download.

Extra Questions For Practice

1. In triangle ABC, right-angled at C, AC + BC = 25 cm and AB = 5 cm. Determine the values of sin A, cos A, and tan A.

2. Find the value of 2 tan² 45° + cos 230° – sin²60°.

3. Find the value of cos² 67° – sin² 23°.

4. In a right triangle PQR, right-angled at Q, if tan P = 1, then verify that 2 sin P cos P = 1.

5. What would be the output if you increase the value of the cosine function from 0° to 90°?

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We believe that an interactive platform teamed with intellectual faculties is where learning takes a turning point. To do so, we provide Class 10 Maths Chapter 8 Notes which consist of brief descriptions of all topics covered in a chapter.

Trigonometry functions demand you to think logically and rationally; hence, we urge you to refer to our revision notes to get these insights. Furthermore, we have revision notes for additional courses and classes. Are you still unsure? Download our revision notes PDF right now and see for yourself.

Conclusion 

The revision notes for CBSE Class 10 Maths Chapter 8 - "Introduction to Trigonometry" offer a concise and valuable resource for students to reinforce their understanding of fundamental trigonometric concepts. These notes distill the key principles, formulas, and applications of trigonometry, providing a quick recap of the chapter's core content. By condensing complex ideas into a succinct format, these notes facilitate efficient revision, aiding students in retaining essential information before exams. The clarity and comprehensiveness of the revision notes empower students to navigate trigonometry-related challenges with confidence, ensuring a strong foundation for further mathematical exploration and success.