Vereshchagin's Collection of Questions and Problems in Plane Trigonometry
by I. P. Vereshchagin
Translated by Valery Manokhin, PhD
A classical Russian problem book in plane trigonometry, in English for the first time. Questions and problems organised to carry a student from the definitions of the trigonometric functions through identities, equations, and the solution of triangles — the problem-solving companion to a classical trigonometry course.
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 physics section reaches AP Physics 1 |
|---|---|---|
| United Kingdom | Years 11–13 | GCSE Higher → A-level Pure and Mechanics |
| Canada | Ontario 10–12 | MPM2D → MCR3U → MHF4U; physics section pairs with SPH3U/SPH4U |
Not covered in this book
graphs of the trigonometric functions and radian measure · statistics and data handling · probability
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Problems to work alongside it
- Derzhavin's Trigonometry$54.95
- Rashevsky's Trigonometry$39.95
Table of contents
27 section headings — the printed contents page in full.
Translator's Preface
PART I. GONIOMETRY.
Chapter I.9 sections
- § 1. Introduction to the trigonometric functions of an arc.
- § 2. Variation of the trigonometric functions under variation of the arc and reduction of the trigonometric functions of an arc greater than 90 degrees to the trigonometric functions of an arc less than 90 degrees and 45 degrees.
- § 3. Relation between the trigonometric quantities of one and the same arc.
- § 4. Trigonometric functions of the sum and difference of arcs.
- § 5. Trigonometric Functions of Multiple Arcs and of Half an Arc.
- § 6. Sum and difference of trigonometric quantities.
- § 7. Sums of the Trigonometric Functions of the Angles of a Triangle.
- § 8. Sums of the trigonometric quantities of four angles whose sum is equal either to 4d, or 2d.
- § 9. Sums of trigonometric quantities of arcs following in arithmetic progression.
Chapter II. Numerical values of the trigonometric lines and their logarithms; use of logarithmic trigonometric tables; trigonometric equations.5 sections
- § 10. Computation of the logarithms of trigonometric quantities.
- § 11. Determination of arcs from the given logarithms of their trigonometric functions and from the given trigonometric functions of these arcs.
- § 12. Computation of expressions in which trigonometric quantities occur; computation of angles whose trigonometric quantity is given in a more or less complicated form.
- § 13. Computation by the method of introducing an auxiliary angle.
- § 14. Solution of trigonometric equations.
PART II. TRIGONOMETRY. SOLUTION OF TRIANGLES.
Chapter I. Solution of right triangles. Solution of isosceles triangles. Regular polygons and the circle.3 sections
- § 15. Fundamental problems on the solution of right triangles.
- § 16. Problems on solving isosceles triangles.
- § 17. Circle and Regular Polygons.
Chapter II. Solution of Oblique Triangles (Principal Cases).4 sections
- § 18. Solution of a Triangle from a Given Side and the Two Adjacent Angles.
- § 19. Solution of a triangle from two given sides and the angle included between them.
- § 20. Solution of a Triangle from the Three Given Sides.
- § 21. Solution of a triangle from two given sides and the angle opposite one of them.
Chapter III. Special Cases in the Solution of Triangles.3 sections
- § 22. Right and Isosceles Triangles.
- § 23. Oblique Triangles.
- § 24. Problems in Practical Geometry.
Chapter IV. Mixed Problems.3 sections
- § 25. Various Problems Relating to All Sections.
- § 26. Problems in solid geometry.
- § 27. Principal questions in physics solved by means of trigonometry.
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $49.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $54.95 | 978-1-919012-58-2 | Amazon | Buy → |
| Hardcover | $84.95 | 978-1-919012-59-9 | 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
- First published
- 2026-08-24
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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