# 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**

**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

- 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:**

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

Angles in Degrees | |||||

Not Defined | |||||

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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

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