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Mathematics · Class 10 · Chapter 30: Introduction to Trigonometry

8 min

Key points

Trigonometry is the study of relationships between angles and sides of triangles
Six trigonometric ratios exist: sine, cosine, tangent, cosecant, secant, and cotangent
In a right-angled triangle, hypotenuse is the longest side opposite to the right angle
Perpendicular is the side opposite to the angle under consideration
Base is the side adjacent to the angle under consideration (excluding hypotenuse)
All trigonometric ratios are dimensionless quantities
sin²θ + cos²θ = 1 is the fundamental trigonometric identity
Complementary angles satisfy: sin θ = cos (90° - θ)
Values of trigonometric ratios for 0°, 30°, 45°, 60°, and 90° must be memorized

Definitions

Trigonometry: Trigonometry is a branch of mathematics which deals with the relationship between angles and sides of a triangle.
Sine Ratio: In a right-angled triangle, sine of an angle is defined as the ratio of the perpendicular to the hypotenuse. sin θ = perpendicular/hypotenuse
Cosine Ratio: In a right-angled triangle, cosine of an angle is defined as the ratio of the base to the hypotenuse. cos θ = base/hypotenuse
Tangent Ratio: In a right-angled triangle, tangent of an angle is defined as the ratio of the perpendicular to the base. tan θ = perpendicular/base
Complementary Angles: Two angles are called complementary if their sum is 90°.

Worked example

In a right triangle ABC, right angled at B, if AB = 3 cm and BC = 4 cm, find all six trigonometric ratios of angle A. (6 marks)

sin A = 4/5, cos A = 3/5, tan A = 4/3, cosec A = 5/4, sec A = 5/3, cot A = 3/4

Common mistakes

Students often confuse perpendicular and base when angle position changes
Forgetting to identify hypotenuse correctly (always opposite to right angle)
Not using Pythagoras theorem when one side is missing
Mixing up reciprocal ratios (cosec, sec, cot) with basic ratios
Incorrect memorization of standard angle values (30°, 45°, 60°)

Quick recap

Trigonometry deals with relationships between sides and angles of right triangles. The six trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. These ratios are defined as specific fractions involving opposite side, adjacent side, and hypotenuse relative to a given acute angle. The fundamental identity sin²θ + cos²θ = 1 is crucial for solving problems.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.