This book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion.
Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown.
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Contents:PrefaceIntroduction: A Review of Some Geometrical IdeasPythagoras' TheoremDegrees versus RadiansCartesian and Polar Coordinates. The Sine and Cosine RatiosThe Cosine RuleStewart's Theorem. Medians and the Centroid GThe Circumcentre, O. The Sine RuleArea. Hero's FormulaThe Tangent RatioSome Very Special AnglesCosecant, Secant, Cotangent. Proving Simple IdentitiesFurther Problems — Heights & DistancesThe Factorisation Formulae & Napier's Tangent RuleAddition Formulae for Sines & CosinesAddition Formulae for TangentsFurther Half-Angle FormulaeSolving the Equation a sin θ + b cos θ = cPtolemy's TheoremMorley's Trisector TheoremCyclic Quadrilaterals and Brahmagupta's FormulaGraphs of the Six Trigonometrical RatiosGraphs of the Six Inverse Trigonometrical RatiosAddition Formulae for Inverse Functions & Rutherford's and Machin's FormulaeSolving Simultaneous EquationsThe Problem of EliminationAngle Bisectors and the Incentre, IAltitudes, the Orthocentre, H and the Pedal TriangleThe Distances OIv, OH, IHExternal Angle Bisectors and the Ex-Centres Ia, Ib, IcThe Distances AIa, OIa, HIaThe Nine-Point Centre, N. The Feuerbach CircleThe Distances IG, INNapoleon Circles and the Fermat PointSmall Angles in RadiansEuler's Product. A Limit for πAngle of Dip and Distance to HorizonA Series for πStricter Inequalities. More LimitsAppendix A Elementary Spherical TrigonometryAuthor IndexBook ReferencesAppendix B More Exercises for PracticeAppendix C Solutions to the More Exercises for Practice
Readership: Students, educators and general public interested in trigonometry.
Solution of Plane Triangles;Associated Points;Addition Formulae;Identities & Equations;Spherical TrianglesKey Features:Mathematical conciseness ( a not too common feature in other books, esp. in the US)Range of topics(seemingly only possible in the much older, but now dated books)Exercises and the full solutions to the problems
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