Table Of ContentT 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 mathe-
matics 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 exer-
cises 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 follow-
ing 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-
>
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