Davidov's Beginnings of Trigonometry
by A. Yu. Davidov
Translated by Valery Manokhin, PhD
Plane and spherical trigonometry in one course, by the founding president of the Moscow Mathematical Society, in first complete English translation. Three parts and 97 numbered sections. Goniometry builds the trigonometric lines from geometric construction, follows them through the whole circle, and treats the addition, multiplication and division of arcs and the construction and use of trigonometric tables, Lalande’s and the seven-digit tables among them. Plane trigonometry solves right and oblique triangles and applies them to measurement: inaccessible distances and heights. Spherical trigonometry derives the fundamental formulas, Delambre’s formulas and Napier’s analogies, solves right and oblique spherical triangles and finds the area of a spherical triangle. A seven-part Supplement takes up inverse trigonometric functions, De Moivre’s formula, the roots of xᵐ = 1, regular polygons, the cubic equation solved by trigonometric lines, and the expansion of the functions into series. Sixty figures, and 265 problems, 212 of them answered in the key at the back.
8 chapters · 97 numbered articles · 265 exercises · 176 pages
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | 10–12 + | Trigonometry / Precalculus; the spherical part and the Supplement go beyond any school course |
|---|---|---|
| United Kingdom | Years 10–13 | GCSE Higher → A-level Pure; De Moivre’s formula and roots of unity are Further Maths |
| Canada | Ontario 10–12 | MPM2D → MCR3U → MHF4U · QC Secondary IV–V SN |
Not covered in this book
graphs of the trigonometric functions and radian measure · statistics and data handling · probability · vectors
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Work through first
- Elementary Algebra$69.95
- Davidov's Algebra$59.95
- Kiselev's Algebra II$54.95
Covers much of the same ground
- Derzhavin's Trigonometry$54.95
Derzhavin is plane trigonometry only, in 192 pages and 86 numbered sections. It opens with the derivative and binds in Tables I–V at the back, which this book does not, and has no spherical trigonometry.
Anoshchenko is plane trigonometry only — 188 pages in three parts and 25 chapters — with supplementary articles on maxima and minima that this book does not have, and no spherical trigonometry.
Rybkin's is plane trigonometry only — 117 pages, 126 numbered sections — with no spherical part and no exercise sets, but it gives trigonometric equations a chapter of their own, which this book does not.
- Rashevsky's Trigonometry$39.95
Rashevsky is the short course — 81 pages to 176 — and plane trigonometry only: no spherical part and no Supplement.
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
Problems to work alongside it
What comes next
- Kiselev's Calculus$54.95
Table of contents
40 section headings — the printed contents page in full.
Translator's Preface
Part I, Chapter 1. On Trigonometric Lines11 sections
- Introduction
- Measure of angles
- Trigonometric functions and trigonometric lines
- Problems
- Relations between the trigonometric lines
- Problems
- Extension of the concept of trigonometric lines to angles greater than a right angle
- Changes in the trigonometric lines as the angle increases from 0 to 2π
- Reduction of the trigonometric lines of an angle greater than a right angle to the trigonometric lines of an acute angle
- Inverse trigonometric functions
- Problems
Part I, Chapter 2. Addition, Multiplication, and Division of Arcs5 sections
- Addition of Arcs
- Multiplication of arcs
- Division of arcs
- Expression of the sum and difference of trigonometric lines by means of a product
- Problems
Part I, Chapter 3. On Trigonometric Tables6 sections
- Calculation of trigonometric lines
- Construction of trigonometric tables
- Lalande’s tables
- Seven-digit tables
- Reduction of formulas to a form convenient for logarithmic computation
- Problems
Part II, Chapter 1. Solution of Right Triangles
Part II, Chapter 2. Solution of Oblique Triangles2 sections
- Relations between the sides and angles of an oblique triangle
- Solution of oblique triangles
Part II, Chapter 3. Applications1 section
- Problems
Part III, Chapter 1. Relations between the Sides and Angles of a Spherical Triangle4 sections
- Spherical triangle
- Fundamental formulas of spherical trigonometry
- Delambre’s formulas
- Napier’s analogies
Part III, Chapter 2. Solution of Spherical Triangles4 sections
- Solution of a right triangle
- Solution of oblique spherical triangles
- Determination of the area of a spherical triangle
- Problems
Supplement7 sections
- I. Inverse trigonometric functions
- II. De Moivre’s Formula
- III. Multiplication and division of arcs
- IV. Roots of the equation xᵐ = 1
- V. On regular polygons
- VI. Solution of an equation of the 3rd degree by means of trigonometric lines
- VII. Expansion of trigonometric functions into series
Solutions of Problems
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $49.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $59.95 | 978-1-80910-024-5 | Amazon | Buy → |
| Hardcover | $94.95 | 978-1-80910-025-2 | Amazon | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 176 pages
- First published
- 2026-10-05
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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