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T H TA B L E S I CUSKiCOLUM anmniMis WITH TABLES By A. M. WELCHONS 'I and W. R. KRICKENBERGER GINN AND COMPANY BOSTON NEW YORK CHICAGO ATLANTA DALLAS COLUMBUS PALO ALTO TORONTO LONDON ©COPYRIGHT, 1957,BYGINNAND COMPANY COPYRIGHT, 1954,BYGINNANDCOMPANY ALLRIGHTSRESERVED 358.9 C : FOREWORD A This text in trigonometry is the outgrowth of the authors’ many years of teaching mathematics in high school. Although it provides, in its entirety, a course that is fully as extensive and rigorous as that usually given in colleges, teachers will find that it was written to meet the needs of high-school students. In its preparation the following objectives have been paramount: 1. The text should create and maintain interest. 2. It should be based upon the students’ background in mathematics and in other fields oflearning. 3. It should develop concepts and principles in such a way that the student can easily understand and apply them. 4. It should offer all possible aid to the teacher. 5. By the sequence and inclusiveness of its subject matter, it should be adaptable to different courses ofstudy. 6. It should provide for individual differences in the abilities of students. The following paragraphs suggest some of the ways in which it is hoped that these aims have been realized Motivates the student Thereareabundantapplications ofinterestto thestudent andphoto- graphs which point up the need for mathematics in various trades and professions. Links the new to the old The development of new concepts is based upon the students’ previous experience in mathematics. Since many students have been introduced to the trigonometry of the right triangle in earlier courses, iii TRIGONOMETRY WITH TABLES IV the approach to the subject is through the acute angle rather than through the general angle. Emphasizes understanding The text is written to the student in language which he can easily understand. New terms are carefully explained, and there are numer- ous examples to illustrate definitions and principles. Care and thor- oughness in presenting the theory lead to understanding rather than to memorization and thus to the ability to make applications. Identities and equations are developed gradually and are fully treated the distinction between them is stressed. ; Helps the teacher The simplicity of organization and presentation will be appreciated by the high-school teacher. A proper balance between the analytical and numerical aspects of trigonometry has been maintained throughout the text. Attention is called to the visual helps, including diagrams, boxed rules, and well-arranged illustrative examples. There are reviews at the ends ofchapters and a set ofgeneral exercises on plane trigonometry. Both four-place and five-place tables are included. Is adaptable to different courses ofstudy The organization and content permit of adaptations to meet the requirements of varying syllabi. At present, trigonometry is taught on two different levels in the secondary schools. In some schools itisoffered inthejunioryear, after intermediatealgebra; in others, it is taught in the last semester ofthe senior year, following solid geometry and advanced algebra. At the earlier level students cannot be ex- pected to cover more than the first ten chapters of this book. At the senior level, because of the students’ maturity and greater experience in mathematics, progress will usually be rapid enough to permit a study ofall the topics. A careful and adequate discussion of approximate numbers is given in Chapter II. FOREWORD V A full treatment ofthe theory and use oflogarithms is provided for the sake of those students who are unfamiliar with this subject. For other students this chapter may be omitted or used for a rapid review. A discussion ofthe use ofthe slide rule is included. It is suggested that students have a slide rule for use in checking solutions and occa- sionally in solving problems involving three significant figures. The treatment of spherical trigonometry is brief and concise, but adequateforapplications to navigation and geography. Providesfor individualdifferences The text is well adapted to classes and students with varying apti- tudes and different levels of preparation. The topics and exercises marked A are intended for all students, while those marked B are for those students who are able to do extra work. Some exceptional students will be able to complete the text in one semester. The following suggestions may be helpful in organizing the semester’s work: A minimum course. Chapters I, II, and IV-X, including only topics marked A and exercises selected from the A group. A medium course. Chapters I-XII, including exercises selected from the A and B groups. A maximum course. Chapters I-XV with selected exercises from the A and B groups. i'u- > Digitized by the Internet Archive in 2017 with funding from University of Alberta Libraries https://archive.org/details/trigonometrywith00welc_0