BooksTrigonometry
Trigonometry books
The classic Russian trigonometry courses and the problem books written to go with them.
8 booksNot sure which one? Where to start →
Trigonometry books: 8 books
Davidov's Trigonometry
by A. Yu. Davidov
US grades 10–12 + · UK Years 10–13
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.
Derzhavin's Trigonometry
by S. S. Derzhavin
US grades 10–12 · UK Years 10–13
A complete classical course in plane trigonometry, in first complete English translation. Eight divisions and 86 numbered sections run from the function concept and radian measure through the trigonometric functions traced quadrant by quadrant, the addition and reduction formulas, the construction and use of logarithmic tables, the solution of oblique triangles by the laws of sines and cosines and by Mollweide’s formulas, measurement in the field and triangulation, the computation of π, and trigonometric equations. Sixty-eight figures and Tables I–V.
Vereshchagin's Plane Trigonometry
by I. P. Vereshchagin
US grades 10–12 · UK Years 11–13
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.
Anoshchenko's Trigonometry
by P. M. Anoshchenko
US grades 10–12 · UK Years 10–13
The 1905 secondary-school course in plane trigonometry, in first faithful English translation from the original Russian edition. Three parts: goniometry builds the measurement of angles and the trigonometric quantities from first principles across twelve chapters; rectilinear trigonometry proper solves the right triangle and then the oblique triangle, and closes with a full chapter on field triangulation; supplementary articles take up trigonometric equations, inverse trigonometric quantities, and maxima and minima. Sixty-three figures on eight plates.
Rybkin's Plane Trigonometry
by N. A. Rybkin
US grades 10–12 · UK Years 10–13
A complete course in plane trigonometry, in first faithful English translation from the original Russian edition. Eleven chapters and 126 numbered sections in three divisions. Goniometry builds the six trigonometric functions from lines in the circle, first for the acute angle and then through the full revolution: reduction formulas, negative angles and periodicity, graphs of the functions, inverse circular functions, the sum and difference, double-angle and half-angle formulas, reduction to logarithmic form and the auxiliary angle, and a chapter of trigonometric equations that shows how roots are lost. The second division explains how trigonometric tables are constructed and how four- and five-place tables are used. The third solves right and oblique triangles, each case worked with natural values and again with logarithms, and closes with measurement in the field: inaccessible distances, heights and triangulation. Fifty-four figures and a summary of the basic formulas.
Rybkin's Trigonometry Problems
by N. A. Rybkin
US grades 10–12 · UK Years 10–13
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.
Rashevsky's Trigonometry
by K. N. Rashevsky
US grades 10–12 · UK Years 10–13
A faithful English edition of the classical Russian trigonometry textbook. A complete course in plane trigonometry — the trigonometric functions, radian measure and the unit circle, identities, equations, and the solution of triangles — built the way the Russian school tradition built it: define, prove, apply.
Schiff's Trigonometry Problems
by V. I. Schiff
US grades 10–12 · UK Years 10–13
A problem book in plane trigonometry by Vera Schiff, who taught mathematics at the Bestuzhev Courses in St Petersburg for thirty-five years, in first faithful English translation from the original Russian edition. 389 numbered problems, with 306 further lettered parts, in ten sections: angles in degrees and radians; the sines and cosines of the simplest angles and the simplest equations; tangent, cotangent, secant and cosecant, with the proof of identities; sums and differences, double, triple and half angles, and sums turned into products; inverse trigonometric functions; the relations between the sides of a triangle and the functions of its angles; logarithmic tables; trigonometric equations; the solution of triangles, including the solids swept out by a triangle turning about an axis; and mixed problems. Answers and worked solutions are given for 209 of the problems.