Chapter 8 — Introduction to Trigonometry

NCERT Class 10 Maths Chapter 8 introduces trigonometry as the study of relationships between the sides and angles of a right triangle, defining six trigonometric ratios — sin, cos, tan, cosec, sec, and cot — and establishing key identities such as sin²A + cos²A = 1.

Chapter 8 of NCERT Class 10 Mathematics covers Introduction to Trigonometry, derived from the Greek words for three, sides, and measure. The chapter defines six trigonometric ratios (sin, cos, tan, cosec, sec, cot) for acute angles of a right triangle, derives their values for standard angles 0°, 30°, 45°, 60°, and 90°, and proves three fundamental trigonometric identities: sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A. Real-life applications such as finding heights and distances are used to motivate the concepts.

1. 01Trigonometry studies relationships between sides and angles of a triangle; the word comes from Greek 'tri' (three), 'gon' (sides), 'metron' (measure).
2. 02Six trigonometric ratios are defined for an acute angle A in a right triangle: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent, with cosec, sec, and cot as their respective reciprocals.
3. 03The values of trigonometric ratios depend only on the angle, not on the size of the right triangle, because similar triangles have proportional sides.
4. 04Standard angle values: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1; cos decreases from 1 to 0 as the angle increases from 0° to 90°.
5. 05Three Pythagorean identities hold for all valid acute angles: sin²A + cos²A = 1, sec²A = 1 + tan²A, and cosec²A = 1 + cot²A.
6. 06If any one trigonometric ratio of an acute angle is known, all remaining five ratios can be determined using definitions and identities.