Chapter 8 — Introduction to Trigonometry

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

• The six ratios — For an acute angle in a right triangle, sides are compared in six ways giving sin, cos, tan and their reciprocals cosec, sec, and cot. These ratios capture how the angle relates to the triangle's sides.
• Ratios depend on the angle alone — Because similar triangles keep sides proportional, a trigonometric ratio depends only on the angle, not the triangle's size. This is why standard angles like 30°, 45°, and 60° have fixed, memorable values.
• The fundamental identities — Three Pythagorean identities connect the ratios, the most basic being sin²A + cos²A = 1. Knowing any one ratio of an angle lets you find all the others using these relationships.

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.