Trigonometrical Ratios Class-9 RS Aggarwal ICSE Maths Goyal Brothers

Trigonometrical Ratios Class-9 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-20. We provide step by step Solutions of Exercise / lesson-20 Trigonometrical Ratios for ICSE Class-9 RS Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe-20 (A), Exe-20 (B), , Exe-20 (C), and  Exe-20 (D), and Notes to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.

Board	ICSE
Publications	Goyal brothers Prakshan
Subject	Maths
Class	9th
Chapter-20	Trigonometrical Ratios
Writer	RS Aggrawal
Book Name	Foundation
Topics	Solution of Exe-20 (A), Exe-20 (B), , Exe-20 (C), and  Exe-20 (D), and Notes to develop skill and confidence
Academic Session	2021-2022

Trigonometrical Ratios Class-9 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-20

---

–: Select Topics :–

Notes on Trigonometrical Ratios

Exe-20 (A),

 Exe-20 (B),

 Exe-20 (C), 

 Exe-20 (D),

---

Notes on Trigonometrical Ratios

The ratio between the lengths of a pair of two sides of a right-angled triangle is called a Trigonometrical Ratio. The three sides of a right-angled triangle give six trigonometrical ratios; namely sine, cosine, tangent, cotangent, secant, and cosecant.

Definition

Trigonometry is the study of relationships between the sides and angles of a triangle

The word “trigonometry” is derived from the Greek words “tri” (meaning three), “gon”(meaning sides) and “metron”(meaning measure)

Right angled triangle ABC

• Side AC is called the hypotenuse of the right angle
• Side AB is called the side adjacent to angle A or base
• Side BC is called the side opposite to angle A or perpendicular

• If we consider angle C, then
  • Side BC is called the side adjacent to angle C
  • Side AB is called the side opposite to angle C

Important properties

• Each trigonometric ratio is a real number and has no unit
• The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains the same
• Since the hypotenuse is the longest side in a right triangle, the value of sin A or cos A is always less than 1 (or, in particular, equal to 1)

Basic Formulas

There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, co-secant, tangent and co-tangent.By using a right-angled triangle as a reference, the trigonometric functions or identities are derived:

• sin θ = Opposite Side/Hypotenuse
• cos θ = Adjacent Side/Hypotenuse
• tan θ = Opposite Side/Adjacent Side
• sec θ = Hypotenuse/Adjacent Side
• cosec θ = Hypotenuse/Opposite Side
• cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

The Reciprocal Identities are given as:

• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• cot θ = 1/tan θ
• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ

For 

(i)            (ii) 

(iii)          (iv) 

(v)        (vi) 

Trigonometry Table

Below is the table for trigonometry formulas for angles that are commonly used for solving problems.

What are the fundamental trigonometry identities?

The three fundamental identities are:

1. sin^2 A + cos^2 A = 1
2. 1+tan^2 A = sec^2 A
3. 1+cot^2 A = csc^2 A

Angles in Degrees
					Not Defined
	Not Defined
					Not Defined
	Not Defined

---

Exe-20 (A),Trigonometrical Ratios Class-9 RS Aggarwal ICSE Maths Goyal Brothers Prakashan  

Page 242-243

Question 1:

Look at the figure given below :

(See in your textbook)

……………….

Question 2:

In the given ……………….. = 3 units.

Find :

(i) sin A

(ii)cos A

……………..

Question 3:

…………………….

…………………….

…………………….

Question 21:

In the given ………………………  lengths of AB and BC.

Question 22:

If cos θ ………….. in θ in terms of x.

---

Trigonometrical Ratios Exe-20 (B) , Class-9 RS Aggarwal ICSE Maths Goyal Brothers Prakashan 

Page 249-250

---

---

 RS Aggarwal Exe-20 (C), Trigonometrical Ratios Class-9  ICSE Maths Goyal Brothers Prakashan 

Page 254-255

Question 1:

(i) ​\( \frac{sin 27^{\circ}}{cos 63^{\circ}} \)​

(ii)…………..

Question 2:

……………

…………….

…………….

Question 14:

Prove that : sin (50 + θ) – ……………… = 0

Question 15:

Prove that : tan (45 – A) …………… = 1

Question 16:

Prove that :

(i)………………

…………………..

 

---

Trigonometrical Ratios Class-9 RS Aggarwal ICSE Maths Goyal Brothers Prakashan  Exe-20 (D),

Page 257

Question 1:

A balloon is connected to a metrological station by a cable …………………. in the string.

Question 2:

A ladder leaning ………………………. of the ladder.

Question 3:

………………………

……………………….

……………………….

Question 6:

In a rectangle ABCD, AB = 12 cm and ………………… side BC and diagonal Ac.

–: End of Trigonometrical Ratios Class-9 RS Aggarwal ICSE Class-9th Maths Solutions   :–

 

Return to-  RS Aggarwal Solutions for ICSE Class-9 Goyal Brothers Prakashan

---

Thanks