APPENDIX, 
APPENDIX A. 
SYNOPSIS OF PLANE TRIGONOMETRY* 
1. Definition. Plane Trigonometry is that branch of mathematical sci 
ence which treats of the relations between the sides and angles of plane 
triangles. It teaches how to find any three of these six parts, when the 
other three are given, and one of them, at least, is a side. 
2. Angles and Arcs. The angles of a triangle are measured by the arcs 
described, with any radius, from the angular points as centers, and inter 
cepted between the legs of the angles. These arcs are measured by com 
paring them with an entire circumference, described with the same radius. 
Every circumference is regarded as being divided into 360 equal parts, called 
degrees. Each degree is divided into 60 equal parts, called minutes, and each 
minute into 60 seconds. These divisions are indicated by the marks ° ' 
Thus 28 degrees, 17 minutes, and 49 seconds, are written 28° 17' 49" Frac 
tions of a second are best expressed decimally. An arc, including a quarter 
of a circumference and measuring a right angle, is therefore 90°. A semi 
circumference comprises 180°. It is often represented by 7r, which equals 
3*14159, etc., or 3f approximately, the radius being 
unity. 
The length of 1° in parts of radius = 0*01745329 ; 
that of 1' = 0*00029089 ; and that of 1" = 0*00000485. 
The length of the radius of a circle in degrees, or 
360ths of the circumference = 57*29578° = 57° 17' 
24*8" = 3437*747' = 206264*8". t 
An arc may be regarded as generated by a point, 
M, moving from an origin, A, around a circle, in the 
direction of the arrow. The point may thus describe 
arcs of any lengths, such as AM; A B = 90° = £ 
tr; A B C = 180° = 7T ; A B C D = 270° = f it ; A B C D A = 360° = 2 tt. 
The point may still continue its motion, and generate arcs greater than a 
* For merely solving triangles, only Articles 1, 2, 3, 6, 6, 10, 11, and 12 are needed. 
•f The number of seconds in any arc which is given in parts of radius, radius 
being unity, equals the length of the arc so given divided by the length of the arc of 
one second; or multiplied by the number of seconds in radius. 
Fig. 410.