Introduction to Trigonometry

Board: GSEB Class: 10

Chapter Overview

Trigonometry deals with relationships between sides and angles of triangles. In a right triangle, the trigonometric ratios are defined: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent, cosec A, sec A, cot A as their reciprocals. The values of ratios for standard angles (0, 30, 45, 60, 90 degrees) must be memorized. The fundamental identity: sin² A + cos² A = 1, as well as 1 + tan² A = sec² A and 1 + cot² A = cosec² A. Trigonometric ratios of complementary angles: sin(90 - A) = cos A, tan(90 - A) = cot A, etc.

Topics Covered

Right Triangle Ratios
Sin, Cos, Tan
Cosec, Sec, Cot
Standard Angle Values
Trigonometric Identities
Complementary Angles
Verification of Identities

Key Formulas

sin A = opposite/hypotenuse

cos A = adjacent/hypotenuse

tan A = opposite/adjacent

sin² A + cos² A = 1

1 + tan² A = sec² A

1 + cot² A = cosec² A

sin(90 - A) = cos A

tan(90 - A) = cot A

Real-World Applications

Applications: Height and distance measurement, navigation, engineering, architecture, astronomy.

Study Tips

Tip: Memorize standard angle table

Tip: Practice proving identities step by step

Tip: Learn complementary angle relationships