112. Sin n a and cos n a expressed in terms of sin a and cos a 113. Comparison of the values of sin a, a, and tan a, a being 126. Definition of spherical right triangle 127. Formulas for the solution of right triangles. 132. Side and angle opposite terminate in same quadrant PLANE TRIGONOMETRY CHAPTER I RECTANGULAR COORDINATES AND ANGLES 1. Introduction. The word trigonometry is derived from the two Greek words for triangle (rpíywvov) and measurement (μerpía). 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 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. and Hence |