Collection of Problems in Trigonometry
by N. A. Rybkin
Translated by Valery Manokhin, PhD
A problem book in trigonometry by the author of the planimetry and stereometry problem collections, in first faithful English translation from the original Russian edition. 1,009 numbered problems in 24 sections and two parts, with an answer key at the back. Part One works through trigonometry itself: the measurement of arcs and angles and radian measure, the variation of the functions, the relations between the functions of one angle, tables of natural values, right and oblique triangles, reduction formulas, the addition theorem, multiple and half arguments, sums turned into products and the auxiliary angle, logarithmic computation, trigonometric equations and inverse circular functions. Part Two applies trigonometry to geometry: plane figures, lines and planes, dihedral and polyhedral angles, the area of a projection, prisms and pyramids, cylinders and cones, volumes, the sphere and solids of revolution. Forty-five figures and a table of natural values.
2 chapters · 24 numbered articles · 1009 exercises · 93 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 | Problem companion to Trigonometry / Precalculus; Part Two reaches solid geometry (G-GMD) |
|---|---|---|
| United Kingdom | Years 10–13 | GCSE Higher → A-level Pure; the solid-geometry part goes past both |
| Canada | Ontario 10–12 | MPM2D → MCR3U → MHF4U · BC Geometry 12 |
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 →Problems to work alongside it
- Derzhavin's Trigonometry$54.95
- Davidov's Trigonometry$49.95
- Kiselev's Stereometry$49.95
- Rashevsky's Trigonometry$39.95
Table of contents
24 section headings — the printed contents page in full.
Translator's Preface
Part One. Trigonometry15 sections
- § 1. Measurement of arcs and angles
- § 2. Variation of trigonometric functions with variation of the angle
- § 3. Relations between the trigonometric functions of one and the same angle
- § 4. Functions of complementary and supplementary angles
- § 5. Tables of natural values of the trigonometric functions
- § 6. Solution of right triangles
- § 7. Solution of oblique triangles
- § 8. Reduction formulas
- § 9. Addition theorem
- § 10. Multiplication and division of the argument
- § 11. Transformation of an algebraic sum of trigonometric functions into a product. Auxiliary angle
- § 12. Application of logarithmic tables to the calculation of trigonometric expressions and to the determination of angles
- § 13. Solution of oblique triangles using logarithms
- § 14. Trigonometric equations
- § 15. Inverse circular functions
Part Two. Problems in geometry requiring the application of trigonometry9 sections
- § 15a. Plane geometry
- § 16. Lines and planes
- § 17. Dihedral and polyhedral angles
- § 18. Area of the projection of a figure on a plane
- § 19. Parallelepipeds, prisms, pyramids and their surfaces
- § 20. Cylinder, cone, frustum of a cone and their surfaces
- § 21. Computation of volumes
- § 22. The sphere and its parts
- § 23. Solids of revolution
Table of trigonometric functions
Answers
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $44.95 | 978-1-919012-90-2 | Amazon | Buy → |
| Hardcover | $69.95 | 978-1-919012-91-9 | 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
- Print length
- 93 pages
- First published
- 2026-09-28
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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