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ICSE Class 9 Mathematics Revision Notes Chapter 22 - Trigonometrical Ratios

Q: 3. Following the concepts from Class 9 Maths Chapter 22, if sin A = 35, find the values of the rest five trigonometric functions.

Here we are given, sin A = \[\frac{3}{5}\].Then as we know, sin A = \[\frac{\text{1}}{\text{cosecA}}\]. So, cosec A= \[\frac{5}{3}\].Now, sin A = \[\frac{\text{perpendicular}}{\text{hypotenuse}}\]. So from this data, we understand that perpendicular = 3, hypotenuse = 5.Let the base be x.Applying Pythagoras theorem,i.e., (perpendicular)2 + (base)2 = (hypotenuse)2We get, (3)2 + (x)2 = (5)2 9 + x2 = 25 x2 = 25 - 9 x2 = 16Thus, x= 4. So we get, cos A = \[\frac{4}{5}\], sec A = \[\frac{5}{4}\], tan A = \[\frac{3}{4}\]and cot A = \[\frac{4}{3}\].

ICSE

ICSE Class 9 Mathematics Revision Notes Chapter 22 - Trigonometrical Ratios

Last updated date: 27th Apr 2024

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Revision Notes for ICSE Class 9 Mathematics Chapter 22 - Free PDF Download

Free PDF download of Class 9 Mathematics Chapter 22 - Trigonometrical Ratios (Sine, Consine, Tangent of an Angle and their Reciprocals) Revision Notes & Short Key-notes prepared by our expert Math teachers as per CISCE guidelines. To register Maths Tuitions on Vedantu.com to clear your doubts.

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ICSE Class 9 Mathematics Revision Notes Chapter 22

Any high achiever goes through the regular pain of highlighting the important points, looking up varied solutions to find the one which is an apt one, figuring out tricks to keep the formulas in mind and then finally practising the test. But guess what, Vedantu is providing all that just for free! Our expert teachers bring you well-written keynotes, solved questions and sample papers for ICSE Class 9 Mathematics chapter 22 - Trigonometric ratios so you get to practice and ace the exams. You get to enjoy these offline or online.

Introduction to the Chapter

In the introduction, the students learn about ‘Trigonometry’ which means the measurement of triangles and how in this chapter, they will only be dealing with the relations of sides and angles of right-angled triangles. On moving forward, the students come across concepts such as perpendicular, base and hypotenuse which are nothing but varied parts of a right-angled triangle. On diving deeper, we learn that for any acute angle (which is also known as angle of reference) in a right-angled triangle; the side opposite to the acute angle is called the perpendicular; the adjacent side to it is called the base and the side opposite to it is called the hypotenuse and their examples.

The next section is about the notation of angles and how they are denoted by Greek letters such as θ(theta), ϕ(phi), (alpha), β(beta), (gamma), etc. Then comes the trigonometrical ratios defined as the ratio between the measurements of a pair of two sides of a right-angled triangle and how they are named sine, cosine, tangent, cotangent, secant, and cosecant. In short, these ratios are written as sin, cos, tan, cot, sec, cosec respectively. The chapter comes to an end with the formulas for individual trigonometric ratios and their reciprocal relations with each other for example:

sinA = \[\frac{\text{perpendicular}}{\text{hypotenuse}}\] and cosecA = \[\frac{\text{hypotenuse}}{\text{perpendicular}}\]

Thus, sin A and cosec A are reciprocal of each other or mathematically,

sin A = \[\frac{\text{1}}{\text{cosecA}}\] and cosec A = \[\frac{\text{1}}{\text{sinA}}\].

Students should note that the trigonometric ratios do not have any unit whatsoever as they are real numbers.

FAQs on ICSE Class 9 Mathematics Revision Notes Chapter 22 - Trigonometrical Ratios

1. What are the different reciprocal relations between the trigonometric ratios in Chapter 22 of Class 9?

There are six trigonometric ratios and their reciprocal relations are as follows:

sin A =\[\frac{\text{perpendicular}}{\text{hypotenuse}}\] and cosec A = \[\frac{\text{hypotenuse}}{\text{perpendicular}}\]

or sin A = \[\frac{\text{1}}{\text{cosecA}}\] and cosec A = \[\frac{\text{1}}{\text{sinA}}\].

Likewise, cosA = \[\frac{\text{base}}{\text{hypotenuse}}\] and secA = \[\frac{\text{hypotenuse}}{\text{base}}\]

Or cos A = \[\frac{\text{1}}{\text{secA}}\] and sec A =\[\frac{\text{1}}{\text{cosA}}\].

and tan A = \[\frac{\text{perpendicular}}{\text{base}}\] and cot A = \[\frac{\text{base}}{\text{perpendicular}}\]

Or tan A = \[\frac{\text{1}}{\text{cotA}}\] and cot A = \[\frac{\text{1}}{\text{tanA}}\].

From the above points, we can also gather that

tan A = \[\frac{\text{sinA}}{\text{cosA}}\] and cot A = \[\frac{\text{cosA}}{\text{sinA}}\].

2. Is learning trigonometric formulas tough for Class 9 students?

At first, students might get a little overwhelmed by the various trigonometric formulas and their usage but through regular practice, sample tests and revision of well-provided free PDF notes from Vedantu which are easy to download from Vedantu’s website or app, made by our experienced scholars for Class 9 Mathematics for Chapter 22 - Trigonometric ratios as per ISCE guidelines, anyone can notice the change happen and get the best results in ICSE board and get perfect scores every student deserves.

3. Following the concepts from Class 9 Maths Chapter 22, if sin A = 35, find the values of the rest five trigonometric functions.

Here we are given, sin A = \[\frac{3}{5}\].

Then as we know, sin A = \[\frac{\text{1}}{\text{cosecA}}\]. So, cosec A= \[\frac{5}{3}\].

Now, sin A = \[\frac{\text{perpendicular}}{\text{hypotenuse}}\].

So from this data, we understand that

perpendicular = 3, hypotenuse = 5.

Let the base be x.

Applying Pythagoras theorem,

i.e., (perpendicular)² + (base)²= (hypotenuse)²

We get, (3)² + (x)² = (5)²

9 + x² = 25

x²= 25 - 9

x² = 16

Thus, x= 4.

So we get,

cos A = \[\frac{4}{5}\], sec A = \[\frac{5}{4}\], tan A = \[\frac{3}{4}\]and cot A = \[\frac{4}{3}\].

4. Following the concepts from Class 9 Maths Chapter 22, name and explain the terms related to a Right-angled triangle.

The Right-angled triangle has 3 sides. Each of these sides is the basis of trigonometric ratios. They are known as base, hypotenuse and perpendicular.

Base - The side adjacent to the angle of reference or also known as the acute angle is known as the base of the right-angled triangle.

Hypotenuse - The side which is opposite to the right angle or the angle which measures 90 degrees, is known as the hypotenuse.

Perpendicular- The side opposite to the angle of reference or acute angle i.e., angle less than 90 degrees is known as the perpendicular.

5. In what ways can ICSE Mathematics Chapter 22 - Trigonometric Ratio serve a practical purpose?

Trigonometry is a very important aspect in architecture such as it can be used to roof a house or to make the roof inclined as in the case of single individual villas and the height of the roof in buildings etc. It is used in the transportation industry. It is used for cartography or the creation of maps. Also, trigonometry is used in satellite systems. It is even used in coding to find the distance between objects in a game or data analysis.