Plane Trigonometry: Classical Russian Mathematics textbook (Russian Math Classics — English Editions)

A classical course in plane trigonometry by Nikolai Aleksandrovich Rybkin (1861-1919), a Russian mathematics educator and author of school textbooks and problem collections.

Plane Trigonometry develops the subject as a connected sequence rather than a list of formulas. It begins with the purpose of trigonometry, functions, arcs, and angles; constructs sine, cosine, tangent, cotangent, secant, and cosecant from the geometry of the circle; then carries the reader through the full circle, negative and beyond-one-revolution angles, periodicity, reduction formulas, inverse functions, graphs, and fundamental identities.

Later chapters treat sums and differences, double and half angles, transformations for logarithmic calculation, trigonometric equations, the construction and use of trigonometric tables, right and oblique triangles, and practical field measurement.

WHY THIS BOOK MATTERS

Rybkin's work reflects a mathematical tradition in which definitions, figures, derivations, computation, and application belong together. A relation is introduced geometrically, proved or transformed, and then used to solve a calculation or measurement problem. That progression makes the book useful both as a historical mathematics text and as a disciplined course of study.

WHAT'S INSIDE

- Six trigonometric functions developed from the circle
- Degrees, radians, periodicity, signs, and reduction formulas
- Identities involving sums, differences, double angles, and half angles
- Logarithmic methods and trigonometric tables
- Trigonometric equations
- Solution of right and oblique triangles
- Field measurement, heights, distances, and triangulation
- Basic trigonometric formulas, worked examples, tables, and numbered figures

This translation preserves the author's sequence, section numbering, definitions, derivations, examples, formulas, tables, cross-references, and figure sequence. Terminology is rendered in standard English usage, while the mathematical progression remains intact.

WHO THIS IS FOR

- Students building a rigorous foundation in trigonometry
- Teachers and tutors using a classical or proof-minded course
- Readers interested in the history of mathematics education
- Adult self-learners who want a structured treatment of functions, identities, equations, and triangle-solving

Translated by Valery Manokhin, PhD.

Published by Northern Star Academic.

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