Degree I INTRODUCTION Degree, in trigonometry, arc equaling 1/360 of the circumference of a circle, or the central angle subtended by such an arc.

Degree I INTRODUCTION Degree, in trigonometry, arc equaling 1/360 of the circumference of a circle, or the central angle subtended by such an arc. The degree is the common unit of measurement for angles and for arcs of a circle. It is divided into 60 minutes, each equal to 1/21,600 of the circumference of a circle; each minute is divided into 60 seconds, each equal to 1/1,296,000 of the circumference of a circle. Degrees are usually indicated by the symbol °, minutes by ', and seconds by ", as in 41° 18'09", 41 degrees 18 minutes 9 seconds. Measurement in degrees is widely used in engineering and the physical sciences, particularly astronomy, navigation, and surveying. The usual means of locating a star or a point on the surface of the earth is by its angular distance in degrees, minutes, and seconds from certain fixed reference points or lines. Positions on the surface of the earth are measured in degrees of latitude north and south of the equator and degrees of longitude east and west of the prime meridian, which is usually taken arbitrarily as the meridian that passes through Greenwich, England. II DEGREE OF LATITUDE If the earth were exactly spherical, a degree of latitude would be equal to 1/360 of the circumference of a circle drawn on the surface of the earth and passing through the North and South poles. The earth, however, is flattened at the poles, so that the actual length of a degree, as determined astronomically, varies from the equator to the poles. At the equator a degree of latitude is 110,568.18 m (362,756.5 ft), or about 110.57 km (about 68.7 statute mi). The length of a degree at 45° North or South, the so-called middle degree, is 111,131.9 m (364,606 ft), or about 111.13 km (about 69.13 statute mi). III DEGREE OF LONGITUDE The length of a degree of longitude varies from a maximum value at the equator to zero at the North and South poles. This is because longitude is measured as the arc of a given parallel of latitude, and the circles forming these parallels decrease in radius as their distance from the equator increases. At the equator a degree of longitude equals 112.09 km (69.65 mi), but at 40° North or South, a degree equals 85.99 km (53.43 mi). Longitude is also measured in hours east or west of the prime meridian, with an hour equal to 15 degrees and a minute, to 15 angular minutes. Thus, the longitude of New York City may be stated as 74° or as 4 hr 56 min west of Greenwich. See also Latitude and Longitude. IV OTHER ANGULAR MEASUREMENTS In advanced branches of mathematics, especially those involving calculus, angles are usually measured in units called radians (rad). There are 2 p rad, or about 6.28 rad, in 360°. In military usage, angles are usually measured in mils, especially for artillery aiming. A mil is the measure of a central angle subtended by an arc that is 1/6400 of the circle. One mil equals 0.05625° and is approximately 0.001 rad. Contributed By: James Singer Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.