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

## 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 + x^{2} = 25

x^{2 }= 25 - 9

x^{2} = 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.