CBSE NCERT NOTES CLASS 10 MATHEMATICS CHAPTER 8

INTRODUCTION TO TRIGONOMETRY

Chapter Notes

Measurement of Angle

Trigonometric Functions

Values of trigonometric ratios of some common angles

Important Trigonometric Formulae

CBSE NCERT NOTES CLASS 10 MATHEMATICS CHAPTER 8

INTRODUCTION TO TRIGONOMETRY

Chapter Notes

Measurement of Angle

Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex.

If the direction of rotation is anticlockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative

Degree: If a rotation from the initial side to terminal side isth $\frac{1}{360}$th of a revolution, the angle is said to have a measure of one degree (1°).

One degree is divided into 60 minutes, and a minute is divided into 60 seconds. That is, one sixtieth of a degree is called a minute, written as 1′, and one sixtieth of a minute is called a second, written as 1″.

Trigonometric Functions

Trigonometric ratios for an angle are the ratio of sides of a right angled triangle.

$\mathrm{sin}\mathrm{x}=\frac{\mathrm{p}}{\mathrm{h}}$

$\mathrm{cos}\mathrm{x}=\frac{\mathrm{b}}{\mathrm{h}}$

$\mathrm{tan}\mathrm{x}=\frac{\mathrm{p}}{\mathrm{b}}=\frac{\mathrm{sin}\mathrm{x}}{\mathrm{cos}\mathrm{x}}$

$\mathrm{sec}\mathrm{x}=\frac{\mathrm{h}}{\mathrm{b}}=\frac{1}{\mathrm{cos}\mathrm{x}}$

$\mathrm{cot}\mathrm{x}=\frac{\mathrm{b}}{\mathrm{p}}=\frac{\mathrm{cos}\mathrm{x}}{\mathrm{sin}\mathrm{x}}$

Values of trigonometric ratios of some common angles

 $\mathrm{d}\mathrm{e}\mathrm{g}$ $0$ $30$ $45$ $60$ $90$ $180$ $270$ $360$ $\mathrm{s}\mathrm{i}\mathrm{n}$ $0$ $\frac{1}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{\sqrt{3}}{2}$ $1$ $0$ $-1$ $0$ $\mathrm{c}\mathrm{o}\mathrm{s}$ $1$ $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$ $0$ $-1$ $0$ $1$ $\mathrm{t}\mathrm{a}\mathrm{n}$ $0$ $\frac{1}{\sqrt{3}}$ $1$ $\sqrt{3}$ $\mathrm{n}\mathrm{d}$ $0$ $\mathrm{n}\mathrm{d}$ $0$ $\mathrm{c}\mathrm{o}\mathrm{t}$ $\mathrm{n}\mathrm{d}$ $3$ $1$ $\frac{1}{\sqrt{3}}$ $0$ $\mathrm{n}\mathrm{d}$ $0$ $\mathrm{n}\mathrm{d}$ $\mathrm{s}\mathrm{e}\mathrm{c}$ $1$ $\frac{2}{\sqrt{3}}$ $\sqrt{2}$ $2$ $\mathrm{n}\mathrm{d}$ $-1$ $\mathrm{n}\mathrm{d}$ $1$ $\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}$ $\mathrm{n}\mathrm{d}$ $2$ $\sqrt{2}$ $\frac{2}{\sqrt{3}}$ $1$ $\mathrm{n}\mathrm{d}$ $-1$ $\mathrm{n}\mathrm{d}$

Some trigonometric identities

$\mathrm{sec}\left(-\mathrm{x}\right)=\mathrm{sec}\mathrm{x}$