While the importance of the function concept for elementary mathematics has become recognized by many writers of college algebra texts and of "unified freshman mathematics" books, it has received little recognition from writers on elementary trigonometry. To emphasize this importance has been the leading motive in writing the present book. A somewhat detailed study of the graphs of the trigonometric functions (Chapter V) and of the inverse functions (Chapter VIII) has been introduced for this purpose. Much more could and should be done in this direction; perhaps the present effort may suffice as a first step.The opportunity afforded by the writing of a new text has been used to make some changes in the presentation of the traditional material. Circular measurement of angles is introduced in the first chapter so as to be available for use throughout the course. The fundamental theorems on projections are presented early and are used subsequently so that the student may be familiar with them when they are applied in a general proof of the addition theorems, based on a method quite generally followed by continental writers. Recognizing the value of the "solution of triangles," a good deal of space has been devoted to this subject, and an attempt has been made to develop it in such a manner that the student can appreciate the reasons for the different methods that are discussed.On the question of " applied problems," I have taken a definite position. I do not think it feasible to introduce into an elementary text technical material from the applied sciences, important though such material may be. Without such material, however, applications cannot well be anything but problems which use the language of the applied sciences without really belonging to them. An elementary text can render useful service, even to applied science, by stressing the fundamental concepts of trigonometry and by setting problems which connect with the student's actual experience and which suggest ways in which these concepts may be applied, leaving actual applications to the fields to which they belong.It has not seemed desirable to add to the number of tables of logarithms already available. The elementary treatment of logarithms in Chapter III and the problems scattered throughout the book call for the use of a set of five-place tables, of which there are many excellent ones in existence.No attempt at logical completeness has been made, but rather has it been my aim to adapt the treatment to the stage of logical development which may be expected of students who begin the study of trigonometry. I am aware of the fact that a fuller discussion might be made in several instances and I shall be happy if the treatment as given should arouse the critical powers of some students and develop in them a desire for more penetrating analysis.The material as here presented was used originally in mimeographed form by a few classes in the University of Wisconsin. I am under a debt of gratitude to the Department of Mathematics for allowing the material to be thus tried out. And it is with special pleasure that I recognize my indebtedness to colleagues in that department and to Professor T. M. Simpson, now of the University of Florida, to some for suggestions and criticisms, to others for assistance in the reading of the proofs. If I add to this my appreciation of the courtesy shown by the publishers of the book, I am ready to rest my case with the jury consisting of the teachers and students of trigonometry.