Textbook in PDF format

Classical course of Trigonometry.
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy.The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions, while the sixth chapter covers the procedures for sketching graphs of trigonometric functions. The coverage of the selection also includes logarithm, solutions of triangles, polar coordinates, and complex numbers.The book will be of great use to both instructors and students of trigonometry.
Much of the traditional matter of trigonometry is still fundamental in modern science and technology. A few of the basic elements of analytic geometry give to trigonometry a more modern flavor but, what is more important, a broader treatment of the trigonometric functions is made possible. Modern trigonometry is analytic trigonometry.
Chapter I introduces some of the essential elements from elementary algebra, plane geometry, and analytic geometry. Chapters II and III present definitions of the trigonometric functions of angles in general, basic identities, and solutions of equations. Trigonometric functions of real numbers are treated in Chapter IV. A one to one identical correspondence between real numbers and measures of angles in radians is established through correspondence of measures of arcs and angles in radians in a unit circle. Real number solutions of equations, including approximation methods, are presented. Chapter V defines inverse trigonometric functions as single-valued functions from the outset. Identities, equations, and methods of expressing general solutions of trigonometric equations are included. A thorough treatment of procedures for sketching graphs of trigonometric functions with analogies from algebra comprises Chapter VI. Chapters VII and VIII cover logarithms and adapt the definitions of the trigonometric functions to the solutions of triangles. Vectors are introduced at this point for use in the problems and because they are needed later in the material on polar coordinates and complex numbers. Applications of the Law of Sines and the Law of Cosines are stressed. The polar coordinate system is introduced in Chapter IX. Here the polar distance is defined and used as a positive number. Chapter X treats complex numbers and series representation. The polar form of a complex number and its vector representation are stressed. Series approximations are included.
Analytic Trigonometry is a study of trigonometry using the methods of analytic geometry whenever appropriate to do so. The word trigonometry comes from the Greek word trigonon meaning triangle and metria meaning measure and was used by Hipparchus in the second century B.C. Ptolemy in the second century A.D. extended the subject using geometry, but it was not until the sixteenth century that Vieta, a Frenchman, employed algebra in the study of trigonometry.
Foundations
Trigonometrie Functions of Angles
Functions of Sums and Related Functions
Trigonometrie Functions of a Number
Inverse Trigonometrie Functions
Sketching Graphs of Trigonometric Functions
Logarithms
Solutions of Triangles
Polar Coordinates
Complex Numbers
Supplement
Analysis Of The Definitions Of The Trigonometric Functions
Answers
Tables