Trigonometry

by

Alfred Monroe Kenyon and Louis Ingold

Contents

• Title Page
• Preface
• Contents

Contents

• Chapter I Introduction
• § 1. Purpose
• § 2. Solution of Triangles
• § 3. Preliminary Esimate. Check
• Exercises I. Graphical Solution of Triangles
• § 4. Squared Paper.    Rectangular Coördinates
• Exercises II. Squared Paper
• Chapter II Right Triangles    Use of Tables
• Part I Fundamental Definitions and Principles
• § 5. Tables
• § 6. Definition of the Ratios
• § 7. Application
• Exercises III. The Trigonometric Ratios
• § 8. Functions of 0° and 90°
• § 9. Construction of Small Tables
• Exercises IV. Solution of Right Triangles
• § 10. The Phythagorean Relations
• Exercises V. The Phythagorean Relations.    Identities
• Part II Accuracy of Solutions    Applications
• § 11. The Question of Grreater Accuracy
• § 12. Functions of 30°, 45°, and 60°
• § 13. Use of the Large Tables
• Exercises VI. Right Triangles. Large Tables
• § 14. Projections
• § 15. Applicaitons of Projections
• Exercises VII. Projections
• § 16. The Use of Logarigthms
• § 17. Products with Negative Factors
• Exercises VIII. Right Triangles. Miscellaneous Exercises
• Chapter III Solution of Oblique Triangles
• Part I Functions of Obtuse Angles
• § 18. Obtuse Angles
• Exercises IX. Functions of Obtuse Angles
• Part II Fundamental Principles of Solution
• § 19. General Method for Oblique Triangles
• § 20. Case I. Given two Angles and a Side
• § 21. Case II. Given two Sides and the Included Angle
• § 22. Case III. Given the Three Sides
• § 23. Case IV. Given two Sides and an Angle Opposite One
• Exercises X. Given Two Sides and the Angle Oposite One of Them
• § 24. The Law of Sines
• § 25. The Law of Cosines
• Exercises XI. Sine Law. Cosine Law
• Part III Special Logarithmic Methods
• § 26. The Law of Tangents
• § 27. The Tangents of the Half-Angles
• § 28. Second Proof of the Law of Tangents
• Exercises XII. Logarithmic Solution of Case II
• § 29. Logarithmic Solution of Case III
• § 30. Second Method for Finding r
• Exercises XIII. Logarithmic Solution of Case III
• § 31. Logarithmic Solution of Case IV. The Ambiguous Case
• Exercises XIV. Logarithmic Solution of Case IV
• Part IV Applications    Problems
• § 32. Areas of Triangles
• § 33. Composition and Resolution of Forces and Velocities
• Exercises XV. Areas. Forces. Velocities
• Exercises XVI. Miscellaneous Exercises
• Chapter IV Line Segments and Angles
• Part I General Definitions and Principles
• § 34. Directed Lines and Segments. Vectors
• § 35. Geometric Addition of Line Segments
• § 36. Subtraction of Line Segments
• Exercises XVII. Line Segments
• § 37. Rotation. Directed Angles
• § 38. Geometric Addition and Subtraction of Directed Angles
• § 39. Placing Angles on Rectangular Axes
• Exercises XVII. Directed Angles
• § 40. Congruent Angles
• § 41. Properties of Congruent Angles
• Exercises XIX. Congruent Angles
• Part II Angular Speed    Radian Measure
• § 42. Measurement of Angles
• § 43. Radian Measure of Angles
• § 44. Use of Radian Measure
• § 45. Angular Speed
• § 46. Notation
• § 47. Relations between Angular Units
• Exercises XX. Angular Speed. Radian Measure
• Chapter V Functions of Any Angle
• Part I Definitions    Reading of Tables
• § 48. Resolution of Forces. Projections
• § 49. General Definitions. Functions of any Angle
• § 50. Algebraic Signs of the Trigonometri Functions
• Exercises XXI. Functions of the General Angle
• § 51. Reading of Tables. Sine and Cosine of -θ and 90° + θ
• § 52. Sine and Cosine of 180° ± θ and 270° +- θ
• § 53. Extension to Other Functions
• Exercises XXII. Reading of the Tables
• Part II Graphs of Trgonometric Functions
• § 54. Plotting of Values
• § 55. Graphs in Radian Measure
• § 56. Mechanical Construction for sin α
• Exercises XXIII. Graphs of the Trigonometric Functions
• Part III Applications of Large Angles
• § 57. Composition and Resolution of Forces
• § 58. The Projection Theorem
• § 59. Application to Forces and Velocities
• Exercises XXIV. Composition and Resolution of Vectors
• § 60. Uniform Circular Motion
• § 61. Period. Amplitude
• § 62. Vibration. Simple Harmonic Motion
• Exercises XXV. Circulation Motion. Vibration
• Chapter VI The Addition Formulas
• § 63. Reduction of A cos α +- B sin α. Formulas
• § 64. Illustrative Examples
• § 65. Independent Proof of Addition Formulas
• § 66. Extension to Angles of Any Size
• Exercises XXVI. Addition Formulas
• § 67. Functions of the Difference of Two Angles
• § 68. Double Angles
• § 69. Tangent of a Sum or of a Difference
• § 70. Applications
• Exercises XXVII. Secondary Formulas. Applications
• § 71. Functions of Half-Angles
• Exercises XXVIII. Half-Angle Formulas
• § 72. Factor Formulas
• Exercises XXIX. Factoring
• Chapter VII Trigonometry Equations and Inverse Functions
• Part I Identities and Equations
• § 73. Identities in One Variable
• § 74. Elementary Identities
• § 75. Identities in Two Variables
• § 76. Illustrative Example
• Exercises XXX. Trigonometric Identities
• § 77. Conditional Equations
• § 78. Illustrative Examples
• § 79. General Principles
• § 80. Use of the Graph
• Exercises XXXI. Simple Trigonometric Equations
• § 81. Reduction Of Equations to Standard Form
• Exercises XXXII. Reduction of Trgonometri Equations
• § 82. Special Mehods of Solution
• § 83. Graphical Methods
• Exercises XXXIII. Special Methods of Solution
• Part II Inverse Functions    Transcendental Equations
• § 84. Inverse Functions
• § 85. Graphical Representation of Inverse Functions
• § 86. Principal Values
• Exercises XXXIV. Inverse Functions. Graphs
• § 87. Transcendental Equations
• Exercises XXXV. Transcendental Equations
• Chapter VIII Spherical Trigonometry
• Part I Summary of Geometric Theorems
• § 88. Purpose
• § 89. Some Useful Propositions of Solid Geometry
• Part II Fundamental Principles of Solution
• § 90. Fundamental Laws. Law of Cosines. Law of Sines.
• § 91. Solution of Spherical Triangles
• § 92. Temporary Ambiguity
• § 93. The Ambiguous Cases
• § 94. Résumé of Cases
• Exercises XXXVI. Spherical Triangles
• Part III Special Methods for Right Triangles
• § 95. Right Spherical Triangles
• § 96. Napier's Rules
• § 97. Ambiguity
• § 98. Quadrantal and Isosceles Spherical Triangles
• Exercises XXXVII. Right Spherical Triangles
• Part IV Special Logarithmic Methods
• § 99. Tangents of the Half-Angles
• § 100. The Law of Tangents (Napier's Analogies)
• § 101. Solution of Triangles by Logarithms
• Exercises XXXVIII. Solution by Logarithmic Methods
• § 102. Areas of Spherical Triangles
• Exercises XXXIX. Areas of Spherical Triangles
• Logarithmic and Trigonometric Tables

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This facsimile edition prepared by La Monte H.P. Yarroll.