Collection of Problems in Trigonometry

LEARN TRIGONOMETRY BY SOLVING THE PROBLEMS THAT MAKE THE FORMULAS USEFUL.

Nikolai Aleksandrovich Rybkin's Collection of Problems in Trigonometry brings together 1,537 graded problems in a sequence that moves from direct practice to problems requiring several ideas at once. This is the first faithful English translation from the original Russian edition.

Rybkin's method is progression. A technique is introduced in a clear, limited setting, then revisited in problems that require recognition, choice of method, calculation, and verification. The result is not a random exercise bank, but a structured course in mathematical problem solving.

WHAT'S INSIDE

Part I — Trigonometry. Measurement of arcs and angles; changes in trigonometric functions; relations among the functions; natural-value tables; right and oblique triangles; reduction, addition, multiplication, and division formulas; logarithmic calculation; trigonometric equations; and inverse circular functions.

Part II — Geometry requiring trigonometry. Planimetry, lines and planes in space, dihedral and polyhedral angles, projections, parallelepipeds, prisms, pyramids, cylinders, cones, frustums, spheres, volumes, and solids of revolution.

Figures, a table of trigonometric functions, and a complete answer section support the work. The author's sequence, section structure, and problem numbering are retained so the book can serve as both a course of practice and a reference.

WHY THIS COLLECTION MATTERS

A textbook can state an identity; a problem collection teaches the reader when and how to use it. Rybkin connects the formula, the geometric situation, and the numerical or deductive task. Working through the problems trains readers to identify the relation they need, choose a useful representation, carry the calculation through, and check whether the result makes sense.

ABOUT N. RYBKIN

Nikolai Aleksandrovich Rybkin (1861–1919) was a Russian teacher, mathematician, and author of school textbooks and problem collections. He wrote for the classroom and treated a well-chosen problem as a way to develop mathematical thinking. His collections remain valuable because their difficulty grows by combination: early problems establish a technique, while later problems require the reader to bring earlier ideas together.

WHO THIS IS FOR

• Students building a rigorous foundation in trigonometry
• Teachers and tutors who need a carefully graded supply of problems
• Families following a classical or proof-minded mathematics course
• Independent readers who want structured practice rather than a list of formulas

Use it alongside a trigonometry or geometry textbook, or work through it on its own as a concentrated problem-solving course.

Translated by Valery Manokhin, PhD.

More English translations of classical mathematics are available at russianmathbooks.com.