Search results
Results From The WOW.Com Content Network
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [4] It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. [5]
Multiplying that fraction by 360° or 2π gives the angle in degrees in the range 0 to 360, or in radians, in the range 0 to 2π, respectively. For example, with n = 8, the binary integers (00000000) 2 (fraction 0.00), (01000000) 2 (0.25), (10000000) 2 (0.50), and (11000000) 2 (0.75) represent the angular measures 0°, 90°, 180°, and 270 ...
One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees. Fractions of a degree may be written in normal decimal notation (e.g., 3.5° for three and a half degrees), but the "minute" and "second" sexagesimal subunits of the "degree–minute–second" system (discussed ...
Decimal degrees are an alternative to using sexagesimal degrees (degrees, minutes, and seconds - DMS notation). As with latitude and longitude, the values are bounded by ±90° and ±180° respectively. Positive latitudes are north of the equator, negative latitudes are south of the equator.
Solid angles can also be measured in square degrees (1 sr = (180/ π) 2 square degrees), in square arc-minutes and square arc-seconds, or in fractions of the sphere (1 sr = 1 / 4 π fractional area), also known as spat (1 sp = 4 π sr). In spherical coordinates there is a formula for the differential,
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
Using this standard notation, the argument x for the trigonometric functions satisfies the relationship x = (180x/ π)°, so that, for example, sin π = sin 180° when we take x = π. In this way, the degree symbol can be regarded as a mathematical constant such that 1° = π /180 ≈ 0.0175.
Angles in polar notation are generally expressed in either degrees or radians (2 π rad being equal to 360°). Degrees are traditionally used in navigation, surveying, and many applied disciplines, while radians are more common in mathematics and mathematical physics. [9]