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Gyaan Maths
CBSE · Class 6-10
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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Detailed theory
For an acute angle θ\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
01
sin⁡θ=oppositehypotenuse\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}, cos⁡θ=adjacenthypotenuse\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}, tan⁡θ=oppositeadjacent\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}.
02
csc⁡θ=1/sin⁡θ\csc\theta = 1/\sin\theta, sec⁡θ=1/cos⁡θ\sec\theta = 1/\cos\theta, cot⁡θ=1/tan⁡θ\cot\theta = 1/\tan\theta.
03
sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1.
04
1+tan⁡2θ=sec⁡2θ1 + \tan^2\theta = \sec^2\theta.
05
1+cot⁡2θ=csc⁡2θ1 + \cot^2\theta = \csc^2\theta.
06
Standard values at 0∘,30∘,45∘,60∘,90∘0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ.
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026