reason I have also tried to present the results in such a light as will make them effective tools for the student in his future work.

During the preparation and printing of the book, Prof. J. M. Peirce has kindly given me the benefit of numerous suggestions and criticisms, which have added greatly to its value. Appendix I. is entirely due to him.

Most of the examples contained in the book have been selected from other trigonometries, especially those of Todhunter, Snowball, and Hamblin Smith.

H. N. W.

CAMBRIDGE, MASS., Dec. 3, 1876.

L

PREFACE TO THE REVISED EDITION.

IN this edition all the typographical errors thus far detected have been corrected; a few changes and additions have been made in the examples of right triangles; and answers to most of the examples have been inserted at the end of Appendix II.

A treatise on Spherical Trigonometry has been prepared by the same author, and now constitutes the second part of this volume.

CAMBRIDGE, MASS., Sept. 16, 1879.

H. N. W.

CONTENTS TO PLANE TRIGONOMETRY.

CHAPTER I.

DEFINITIONS AND FIRST PRINCIPLES.

Page.

1

2

§ 2. Line regarded as traced by the movement of a point.

Beginning and end of a line. Addition of lines defined,

§ 3. Direction of a line. Opposite directions indicated by

signsand. Line completely represented by an ex-

pression involving the points at its extremities. For-

mulas for the sum of lines

§ 4. Degree of angle. Degree of arc. Quadrant defined

§ 5. Complement and supplement of an angle or arc defined

§ 6. Circular measure of an angle the ratio of intercepted arc

to radius.

§ 7. Circular measure equal to the length of the intercepted

arc in the unit circle

§ 8. Angular unit of circular measure that angle whose inter-

cepted arc is equal to the radius

§ 9. To change from circular measure to degree measure, and

the converse. Angular unit of circular measure equal

to 57°.2957795. Circular measure of 1°, 1', and 1"

§ 10. Circular measure of 360°, 180°, 90°, and 45°, equal to

§ 11. Angle regarded as the measure of the rotation of a line,

6

§ 12. No limit to angular magnitude. Initial line. Terminal

§ 13. Angle represented by three letters; the order of the let-

ters. Angle represented by two letters. (Peirce, No-

tation.)

§ 14. Positive and negative rotation defined

§ 15. 1st, 2d, 3d, and 4th quadrants defined. Figure for an

angle of each quadrant

§ 16. Addition of angles

§ 17. Remarks about positive and negative angles

8

8

9

9

10

§ 18. Angles and ± k 360° bounded by the same lines

§ 19. Equations obtained by a general application of § 16

§ 20. Rules concerning the directions of certain lines

§ 21. Statement of a few principles of plane geometry to

which it will be necessary to refer hereafter.

Examples

THE TRIGONOMETRIC FUNCTIONS.

§ 22. Triangle of reference formed by letting fall a perpen-

dicular from any point of the terminal line upon the

initial line. Figures. Signs of the sides of a triangle

of reference

§ 23. The Trigonometric Functions defined to be the six ratios

between the three sides of a triangle of reference.

These ratios shown to be always the same for the

same angle, and different for different angles. Reason

for the name "Function"

24. A name given to each of the trigonometric functions.

Versed sine

§ 25. Table of signs of the different functions for an angle

of each quadrant. Sin and cos vary only from - 1 to

+1; sec and csc, from 1 to ∞ tan and ctn,

§ 26. Sin, cos, and tan, reciprocals of csc, sec, and ctn

28. Relations between sin and cos, tan and sec, ctn and csc,

2222

21