Trigonometría Rectilínea de Derzhavin
por S. S. Derzhavin
Traducido por Valery Manokhin, PhD
Un curso clásico completo de trigonometría plana, en primera traducción completa al inglés. Ocho divisiones y 86 secciones numeradas: del concepto de función y la medida en radianes a las fórmulas de adición y reducción, las tablas logarítmicas, la resolución de triángulos oblicuángulos, la medición sobre el terreno y la triangulación, el cálculo de π y las ecuaciones trigonométricas. Sesenta y ocho figuras y las Tablas I–V.
8 capítulos · 86 artículos numerados · 192 páginas
Dónde encaja en el curso escolar — EE. UU., Reino Unido y Canadá ↓ Adultos y autodidactas bienvenidos — las grandes matemáticas no tienen límite de edad.
Dónde encaja en el curso escolar
Plan de estudios completo: todos los libros por curso →| Estados Unidos | 10–12 | Trigonometry / Precalculus; the field-measurement chapter has no modern counterpart |
|---|---|---|
| Reino Unido | Years 10–13 | GCSE Higher (sine and cosine rules) → A-level Pure |
| Canadá | Ontario 10–12 | MPM2D → MCR3U → MHF4U · QC Secondary IV–V SN |
No incluido en este libro
estadística y tratamiento de datos · probabilidad · vectores
Estos bloques habrá que cubrirlos con otro material. Faltan en el libro, no en esta descripción.
Dónde encaja este libro
Ver la secuencia completa →Estudiar antes
- Álgebra Elemental$69.95
- Álgebra II de Kiselev$54.95
Cubre gran parte del mismo temario
Casi la misma extensión —188 páginas frente a 192—, pero Anoshchenko dedica 57 páginas a artículos suplementarios: ecuaciones trigonométricas, cantidades trigonométricas inversas, máximos y mínimos. Este libro les dedica seis secciones numeradas y añade la derivada, las series de seno y coseno, el cálculo de π y las Tablas I–V, que Anoshchenko no trae.
Rashevsky es el curso breve: 81 páginas frente a 192. No trae tablas logarítmicas, ni capítulo de medición sobre el terreno, ni el cálculo de π.
Se solapan en gran medida. Cada nota indica qué trae ese libro que este no — esas diferencias son las que deciden.
Problemas para trabajar en paralelo
Qué viene después
- Cálculo de Kiselev$54.95
Índice
93 secciones — el índice completo del libro impreso.
Translator's Preface
Introduction6 secciónes
- §1. The concept of a function
- §2. Continuous change of the argument and of the function
- §3. Geometric representation of functions
- §4. The concept of the derivative
- §5. Mechanical meaning of the derivative
- §6. Measurement of angles in radians
The concept of trigonometric functions and their variation19 secciónes
- §7. Equation of a circle with center at the origin
- §8. The concept of the functions sin t and cos t
- §9. Positive and negative direction of arcs
- §10. Variation of the function sin t in connection with the variation of the arc from 0 to ± 2kπ
- §11. Table of values of the function sin t
- §12. Graphical representation of the variation of the function sin t
- §13. Variation of the function cos t in connection with the variation of the arc from 0 to ± 2 k π
- §14. Graphical representation of the variation of the function cos t
- §15. The concept of the functions tg t and ctg t
- §16. Variation of the function tg t in connection with the variation of the arc from 0 to ± kπ
- §17. Graphical representation of the variation of the function tg t
- §18. Variation of the function ctg t in connection with the variation of the arc from 0 to ± kπ
- §19. Graphical representation of the variation of the function ctg t
- §20. Expression of tg t and ctg t as functions of sin t and cos t
- §21. The concept of the functions sc t and csc t
- §22. Variation of the functions sc t and csc t in connection with the variation of the arc from 0 to ± 2kπ
- §23. Formulas relating sc t and csc t to the other trigonometric functions
- §24. Relations between the elements of a right triangle
- §25. Solution of right triangles
Transformation of coordinates and identical trigonometric transformations22 secciónes
- §26. Relations between the trigonometric functions of the arcs +t and -t
- §27. Transformation of coordinates
- §28. Reduction formulas for sine and cosine
- §28a. A second method of deriving the reduction formulas for sine and cosine
- §29. Reduction formulas for tangent, cotangent, secant, and cosecant
- §30. The concept of circular functions
- §31. Properties of the circular functions
- §32. General expression for arcs having the same sine or cosecant
- §33. General expression for arcs having the same cosine or secant
- §34. General expression for arcs having the same tangent or cotangent
- §35. Examples
- §36. Transformation of the direction of the coordinate axes
- §37. Sine and cosine of the sum of two arcs
- §38. Sine and cosine of the difference of two arcs
- §39. Tangent of the sum and difference of arcs
- §40. Theorem
- §41. A second method of obtaining the formulas for the sine and cosine of the sum and difference of two arcs
- §42. Generalization of the formulas for the sine and cosine of the sum and difference of two arcs
- §43. Sine, cosine and tangent of double arcs
- §44. Sine, cosine and tangent of half an arc
- §45. Reduction of expressions to a form convenient for logarithmic computations
- §46. Reduction of expressions to logarithmic form by introducing an auxiliary angle
Tables of values of trigonometric functions and their logarithms14 secciónes
- §47. Theorems on which the computation of values of trigonometric functions for small angles is based
- §48. Approximate computation of sin 0.01 and cos 0.01
- §49. Approximate calculation of sin 1' and cos 1'
- §50. Simpson's formulas; their application to the construction of tables of values of trigonometric functions
- §51. Expansion of sin t and cos t into infinite series
- §52. Differences of successive values of sines and cosines
- §53. Tables of logarithms of trigonometric quantities
- §54. Finding the logarithm of a trigonometric function of a given angle
- §55. Theorem
- §56. Finding the logarithms of the sine and tangent for angles close to zero, and also the logarithms of the cosine and cotangent for angles close to a right angle
- §57. Finding an angle from the logarithm of a trigonometric function
- §58. Finding an angle from the logarithm of a trigonometric function in the case of a large tabular difference
- §59. Derivatives of trigonometric functions
- §60. Simple harmonic motion
Solution of oblique triangles12 secciónes
- §61. Theorem. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half the difference of the same angles
- §62. Mollweide's formulas
- §63. Theorem
- §64. Expression of the trigonometric functions of the angles of an oblique triangle in terms of its sides
- §65. Area of a triangle
- §66. Theorem
- §66a. Corollaries
- §67. Solution of oblique triangles
- §68. Numerical examples on the solution of triangles
- §69. Examples of more complicated cases of solving oblique triangles
- §70. Problem
- §71. Solution of regular polygons
Measurements on the ground9 secciónes
- §72. Surveying; vertical and horizontal directions
- §73. Designation and measurement of lines on the ground
- §74. Measurement of angles
- §75. Laying out on the ground mutually perpendicular and parallel lines with the aid of a cross-staff
- §76. Determination of the relative heights of two points
- §77. Application of trigonometry to the performance of various measurements on the ground
- §78. Determination of heights
- §79. Determination of inaccessible distances
- §80. Triangulation
Computation of π3 secciónes
- §81. Addition and subtraction of circular functions
- §82. Expansion of arc tg x in powers of x
- §83. Computation of π
Trigonometric equations3 secciónes
- §84. General remarks
- §85. Examples of trigonometric equations with one unknown
- §86. Examples of solving systems of trigonometric equations with two unknowns
Tables5 secciónes
- Table I
- Table II
- Table III
- Table IV
- Table V
Formatos y ediciones
| Formato | Precio | ISBN-13 | Dónde | Comprar |
|---|---|---|---|---|
| Tapa blanda | $54.95 | 978-1-80910-009-2 | Amazon | Comprar → |
| Tapa dura | $84.95 | 978-1-80910-010-8 | Amazon | Comprar → |
Los precios son los de lista del editor. Amazon fija el precio final en cada tienda.
Detalles del producto
- Editorial
- Northern Star Academic Press
- Idioma
- English
- Traductor
- Valery Manokhin, PhD
- Extensión
- 192 páginas
- Primera publicación
- 2026-09-16
Publicado por Northern Star Academic Press · Primera traducción fiel del original ruso
Más de Esta Serie
1001 Problemas de Rachinsky
por S. A. Rachinsky
Grados 4–8 (EE. UU.) · Years 5–9 (RU)
1.001 problemas cuidadosamente seleccionados del maestro rural cuyos estudiantes fueron retratados en la famosa pintura de 1895 "Aritmética Mental."
Aritmética Recreativa
por Ya. I. Perelman
Grados 4+ (EE. UU.) · Year 5+ (RU)
El clásico de las matemáticas populares rusas. Rompecabezas, acertijos y curiosidades que hacen la aritmética verdaderamente entretenida.
Markov: Probabilidades
por Andrei A. Markov
Grados 12 and university (EE. UU.) · Year 13 and university (RU)
La obra fundacional de 1900 sobre la teoría de la probabilidad por el matemático que nos dio las cadenas de Markov.