The concept of the trigonometric angle is basic to the study of trigonometry. A trigonometric angle is generated by a rotating ray. The rays OA and OB (Fig. 1a, 1b, and 1c) are considered originally coincident at OA, which is called the initial side. The ray OB then rotates to a final position called the terminal side. An angle and its measure are considered positive if they are generated by counterclockwise rotation in the plane, and negative if they are generated by clockwise rotation. Two trigonometric angles are equal if they are congruent and if their rotations are in the same direction and of the same magnitude.

An angular unit of measure usually is defined as an angle with a vertex at the center of a circle and with sides that subtend, or cut off, a certain part of the circumference 
(Fig. 2).


If the subtended arc s (AB) is equal to one-fourth of the total circumference C, that is, s = 3C, so that OA is perpendicular to OB, the angular unit is a right angle. If s = 1C, so that the points A, O, and B are on a straight line, the angular unit is a straight angle. If s = 1/360C, the angular unit is one degree. If s = YC, so that the subtended arc is equal to the radius of the circle, the angular unit is a radian. By equating the various values of C, it follows that 1 straight angle = 2 right angles = 180 degrees = p radians

Each degree is subdivided into 60 equal parts called minutes, and each minute is subdivided into 60 equal parts called seconds. For finer measurements, decimal parts of a second may be used. Radian measurements smaller than a radian are expressed in decimals. The symbol for degree is °; for minutes, '; and for seconds, ". For radian measures either the abbreviation rad or no symbol at all may be used. Thus

 The angular unit radian is understood in the last entry. (The notation 42".14 may be used instead of 42.14" to indicate decimal parts of seconds.)

By convention, a trigonometric angle is labeled with the Greek letter theta (q). If the angle q is given in radians, then the formula s = rq may be used to find the length of the arc s; if q is given in degrees, then