Тригонометрия: основы, тождества и уравнения: концептуальный и графический подход к классической тригонометрии

Trigonometry: Foundations, Identities, and Equations develops trigonometry as a coherent and logically structured subject, rather than a collection of formulas to memorize. Starting from angle measurement and trigonometric ratios, the book builds a solid foundation through systematic development of identities, compound angles, and multiple-angle relationships. Emphasis is placed on understanding why identities hold, how they transform expressions, and how they are applied to solve equations and inequalities in a structured manner. A key feature of the book is its conceptual and graphical approach. Graphs and interval-based reasoning are used to clarify sign conventions, periodic behavior, symmetry, and solution structure, strengthening both intuition and rigor. Reduction formulae, identity proofs, and equation-solving strategies are presented methodically, helping readers avoid common errors. Each chapter includes worked examples, graded exercises, common errors and examiner traps, and self-assessment tests to reinforce understanding. This book is intended for high achievers in IB, AP, and A-Level mathematics, advanced high-school and early undergraduate students, and aspirants of JEE (Main & Advanced) and mathematics Olympiads. It is especially suited for students aiming for the world’s top universities, where strong conceptual understanding and mathematical maturity are essential. This volume is the first part of the Math By Rishabh Series – Trigonometry, followed by Book 2: Trigonometry – Advanced Methods and Olympiad Applications.