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PLANE AND SPHERICAL

TRIGONOMETRY.

BY

G. A. WENTWORTH, A.M.,

PROFESSOR OF MATHEMATICS IN PHILLIPS EXETER ACADEMY.

BOSTON:

PUBLISHED BY GINN, HEATH, & CO.
1882.

HARVARD COLLEGE LIBRARY

GIFT OF

MISS ELLEN L. WENTWORTH

MAY 1939

Entered, according to Act of Congress, in the year 1882, by

G. A. WENTWORTH,

in the office of the Librarian of Congress, at Washington.

GINN, HEATH, & Co., PRINTERS:
J. S. CUSHING, SUPT., 16 HAWLEY STREET,

BOSTON.

PREFACE.

IN

N preparing this work the aim has been to furnish just so much of Trigonometry as is actually taught in our best schools and colleges. Consequently, development of functions in series and all other investigations that are important only for the special student have been omitted. The principles have been unfolded with the utmost brevity consistent with simplicity and clearness, and interesting problems have been selected with a view to. awaken a real love for the study. Much time and labor have been spent in devising the simplest proofs for the propositions, and in exhibiting the best methods of arranging the logarithmic work.

The author is under particular obligation for assistance to G. A. Hill, A.M., of Cambridge, Mass., to whom is chiefly due whatever value the Trigonometry possesses.

PHILLIPS EXETER ACADEMY,
September, 1882.

G. A. WENTWORTH.

CONTENTS.

CHAPTER I. FUNCTIONS OF ACUTE ANGLES:

Definitions, 1; representation of functions by lines, 7; changes in

the functions as the angle changes, 9; functions of complementary
angles, 10; relations of the functions of an angle, 11; formulas for
finding all the other functions of an angle when one function of the
angle is given, 13; functions of 45°, 30°, 60°, 15.

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