# Introduction To Trigonometry Class 10 Notes

## Trigonometry Class 10

Introduction to trigonometry class 10 notes provided here gives an in-depth understanding of this chapter in a concise way. Students can refer these notes to learn the concepts in a better way and use it during revision time and also learn trigonometry formulas. Trigonometry for class 10 chapter 8 notes cover the following-

• What is trigonometry
• Trigonometric ratios
• Trigonometric ratio table
• Some important formulas
• Example Questions
• Practice Questions

## What is Trigonometry?

Trigonometry is the study of relationships between the angles and sides of a triangle. This word is derived from three the Greek words which. ‘tri’ (three), ‘gon’ (sides) and ‘metron’ (measure).

In simple words, trigonometry is the study of relationships between the sides and angles of a triangle. Trigonometry was used to find out the distances of the stars and planets from the Earth in the earlier days.

In a right triangle, the ratio of sides can be represented as a trigonometric angle. We will calculate the ratio of some standard angles and establish identities involving these ratios, known as trigonometric identities.

## Trigonometric Ratios

There are three main trigonometric ratios which are studied in trigonometry class 10:

• Sine θ = Opposite Side / Hypotenuse Side
• Cosine θ = Adjacent Side / Hypotenuse Side
• Tangent  θ = Opposite Side / Adjacent Side

The three inverse functions of the above trigonometric ratios are

• Cosecant θ  =1/ Sin = Hypotenuse Side/ Opposite Sidef
• Secant θ = 1/Cos = Hypotenuse Side / Adjacent Side
• Cotangent θ = 1/tan = Adjacent Side/ Opposite Side

In a right triangle ABC, right-angled at B, Side AB is called as a base(B), BC is called as Perpendicular(P) and side AC is called as Hypotenuse(H).

From the above diagrams, the trigonometric ratios of angle A in the right triangle ABC are defined as follows-

Sin A = BC/AC

Cos A = AB/AC

Tan A = BC/AB

Cosec = AC/BC

Sec A = AC/AB

Cot A =AB/BC

### Trigonometric Ratio Table

 Angle 0° 30° 45° 60° 90° Sin A 0 1/2 1/√2 √3/2 1 Cos A 1 √3/2 1/√2 1/2 0 Tan A 0 1/√3 1 √3 Not Defined Cosec A Not Defined 2 √2 2/√3 1 Sec A 1 2/√3 √2 2 Not Defined Cot A Not Defined d√3 1 1/√3 0

### Trigonometry Class 10 Important Formulas

• sin (90 – A) = cos A
• cos (90 – A) = sin A
• tan (90 – A) = cot A
• cot (90 – A) = tan A
• sec (90 – A) = cosec A
• cosec (90 – A) = sec A.
• sin2A + cos2A = 1
• sec2 A – tan2A = 1 for 0° ≤ A < 90
• cosec2 A = 1 + cot2A for 0° < A ≤ 90

Check out all the important formulas in this article and be able to solve any question easily. These formulas are extremely important and can help students to have a complete understanding of this topic.

### Important Questions

1. Find the value of (sec A + tan A) (1 – sin A)
2. Prove $\frac{Cos\, A}{1+sin\,A}+\frac{1+sin\,A}{cos\,A}=2\,sec\,A$
3. $\frac{1}{tan\,A+cot\,A} = \left ( cosec\,A-sin\,A \right )\left ( sec\,A-cos\,A \right ).$ Prove this.

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