Class 10 · Chapter 8

Introduction to Trigonometry

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

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Mathematics · Class 10 (2026-27)

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Detailed theory

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 triangle's size (similar triangles have equal ratios).

Key concepts & formulas

\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}

\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}

\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}

\csc\theta = 1/\sin\theta

\sec\theta = 1/\cos\theta

\cot\theta = 1/\tan\theta

\sin^2\theta + \cos^2\theta = 1

1 + \tan^2\theta = \sec^2\theta

1 + \cot^2\theta = \csc^2\theta

Standard values at

0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ