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.

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


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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 \theta < 90^o

(i)  sin \ (90^o - \theta) = cos \ \theta            (ii) cos \ (90^o - \theta) = sin \ \theta

(iii) tan \ (90^o - \theta) = cot \ \theta          (iv) cot \ (90^o - \theta) = tan \ \theta

(v)  sec \ (90^o - \theta) = cosec \ \theta       (vi) cosec \ (90^o - \theta) = sec \ \theta

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 (\theta) 0^o 30^o 45^o 60^o 90^o
sin 0 \frac{1}{2} \frac{1}{\sqrt{2}} \frac{\sqrt{3}}{2} 1
cos 1 \frac{\sqrt{3}}{2} \frac{1}{\sqrt{2}} \frac{1}{2} 0
tan 0 \frac{1}{\sqrt{3}} 1 \sqrt{3} Not Defined
cosec Not Defined 2 \sqrt{2} \frac{2}{\sqrt{3}} 1
sec 1 \frac{2}{\sqrt{3}} \sqrt{2} 2 Not Defined
cot Not Defined \sqrt{3} 1 \frac{1}{\sqrt{3}} 0

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


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


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


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

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

 

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