CBSE · Class 6-12

Class 10 · Mathematics (Standard)

Unit 8 · Class 10Mathematics (Standard)

Introduction to Trigonometry

Trigonometric ratios (sin, cos, tan and reciprocals), values at standard angles, and fundamental identities.

Lessons

6 concepts

1
Right Triangle Ratios
For an acute angle $\theta$ in a right triangle, the six trigonometric ratios are defined in terms of opposite side, adjacent side, and hypotenuse. Only the acute angle matters — the ratios are independent of the triangl…
2
Values at Standard Angles
Memorise the table: $\sin 0 = 0, \sin 30 = 1/2, \sin 45 = 1/\sqrt 2, \sin 60 = \sqrt 3/2, \sin 90 = 1$ ; $\cos$ mirrors $\sin$ from the other end ( $\cos 0 = 1, \ldots, \cos 90 = 0$ ); $\tan = \sin/\cos$ .
3
Fundamental Identity
From Pythagoras on a right triangle: $\sin^2\theta + \cos^2\theta = 1$ . Dividing by $\cos^2\theta$ gives $\tan^2\theta + 1 = \sec^2\theta$ ; dividing by $\sin^2\theta$ gives $1 + \cot^2\theta = \csc^2\theta$ .
4
Complementary Angles
For $\theta + \phi = 90^\circ$ : $\sin\theta = \cos\phi$ , $\cos\theta = \sin\phi$ , $\tan\theta = \cot\phi$ , $\sec\theta = \csc\phi$ . E.g. $\sin 20^\circ = \cos 70^\circ$ .
5
Techniques to Prove Identities
Convert everything to $\sin$ and $\cos$ ; use Pythagorean identities to simplify. Sometimes multiplying numerator and denominator by a conjugate (e.g. $\sec\theta + \tan\theta$ ) simplifies. Always work on one side and sho…
6
Finding Other Ratios from One
If one ratio is given (e.g. $\sin\theta = 3/5$ ), form a right triangle with sides matching the ratio, use Pythagoras to find the third side, then read off all other ratios. This is a standard problem type.

Skills to practise

Skill · medium

Introduction to Trigonometry — Practice