SME-SMAD Reference 1, Introduction. The word trigonometry is derived from the two Greek words for triangle (rptyuvov) and measurement (jxcTpta). Originally trigonometry was concerned chiefly with the solution of triangles. At present this is but one part of the subject. Certain preliminary considerations, concerning directed lines and angles, are necessary before introducing the fundamental definitions of trigonometry. RECTANGULAR COORDINATES 2. Directed lines. A positive and a negative direction may be assigned arbitrarily to every line. If the direction from A to C is positive, the opposite direction from C to A is negative. If we let the order of the let- _^ ters indicate the direction in A c which a segment is measured, it is evident that AC and CA represent the same segment measured in opposite directions; hence AC^-CA or -AC= CA. Also, if B be a third point on the line, the segments AB and BA are opposite in sign; likewise the segments BC and CB. Hence AB=~BA or - AB = BA, and BC= Table of Contents 1 Introduction 1; Rectangular Coordinates; 2 Directed lines1; 3 Lines of reference 2; 4 Quadrants 2; 6 Coordinates of a point 2; 0 Signs of coordinates 3; 7 Exercises 8; Angles; 8 Magnitude of angles 4; 9 Direction of rotation Positive and negative angles 4; 10 Initial and terminal lines 6; 11 Sign of terminal line 5; 12 Algebraic sum of two angles 5; 13 Measurement of angles 6; 14 Circular or radian measure 7; 16 Value of radian 7; 16 Relation between degree and radian 7; 17 Relation between angle, radius, and arc ' 9; 18 Linear and angular velocity 9; 19 Examples 10; 20 Trigonometric functions introduced 12; 21 Definitions of the trigonometric functions 12; 22 Values of the trigonometric functions of 30" 45°, and 60° 18; 23 Values of the trigonometric functions of 120°, 135°, and 160° 16; 24 Signs of the trigonometric ratios 17; 25 Trigonometric functions are single valued 18; 26 A given value of a trigonometric function dete