Essentials of plane trigonometry and analytic geometry

246 Pages·2007·6.64 MB·English

by  Antherton H. Sprague

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ESSENTIALS OF
PLANE TRIGONOMETRY
AND
ANALYTIC GEOMETRY

ESSENTIALS OF
PLANE TRIGONOMETRY
AND
ANALYTIC GEOMETRY
BY
ATHERTON H. SPRAGUE
PROFESSOR OP MATHEMATICS
AMHEBST COLLEGE
NEW YORK
PRENTICE-HALL, INC.
1946
COPYRIGHT, 1934, BY
PRENTICE-HALL, INC.
70 FIFTH AVENUE, NEW YORK
ALL RIGHTS RESERVED. NO PARTOFTHISBOOKMATBB
REPRODUCED IN ANY FORM, BY MIMEOGRAPH OR ANT
OTHERMEANS, WITHOUT PERMISSION IN WRITINGFROM
THEPUBLISHERS.
FirstPrinting June, 1934
SecondPrinting April,1936
Third Printing September, 1938
FourthPrinting October, 1939
FifthPrinting April,1944
SixthPrinting August,1946
PRINTEDINTHEUNITEDSTATUSOFAMERICA
PREFACE
THE purpose of this book is to present, in a single
volume, the essentials of Trigonometry and Analytic
Geometry that a student might need in preparing for a
study of Calculus, since such preparation is the main
objective in many of our freshman mathematics courses.
However, despite the connection between Trigonometry
and Analytic Geometry, the author believes in maintaining
a certain distinction between these subjects, and has
brought out that distinction in the arrangement of his
material. Hence, the second part of the book supple-
mented by the earlier sections on coordinate systems,
found in the first part would be suitable for a separate
course in Analytic Geometry, for which a previous knowl-
edge of Trigonometry is assumed.
The oblique triangle is handled by means of the law of
sines, the law of cosines, and the tables of squares and
square roots. However, theusual law of tangents andther
"
formulas are included in an additional chapter, Supple-
mentary Topics."
There is included in the text abundant problem material
on trigonometric identities for the student to solve.
The normal form of the equation of a straight line is
derived in as simple a manner as possible, and the per-
pendicular distance formula is similarly derived from it.
The conies are defined in terms of focus, directrix, and
eccentricity; and their equations are derived accordingly.
" "
In the chapter Transformation of Coordinates are
discussed the general equation of the second degree and
the types of conies arisingtherefrom. Anattempthasbeen
made to present rigorously, but without too many details,
the material necessary for distinguishing between the types
PREFACE
vi
of conies by means of certain invariants, which enter
naturally into the discussion. Although this chapter may
be omitted from the course, it is well included if time
permits.
ATHERTON H. SPBAGUE
Amherst College