Search results
Results from the WOW.Com Content Network
In spherical trigonometry, the law of cosines (also called the cosine rule for sides [1]) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry. Spherical triangle solved by the law of cosines. Given a unit sphere, a "spherical triangle" on the surface of the sphere ...
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
In spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a spherical triangle exceeds 180 degrees.
Spherical trigonometry on Math World. Intro to Spherical Trig. Includes discussion of The Napier circle and Napier's rules; Spherical Trigonometry — for the use of colleges and schools by I. Todhunter, M.A., F.R.S. Historical Math Monograph posted by Cornell University Library. Triangulator – Triangle solver. Solve any plane triangle ...
The excess, or area, of small triangles is very small. For example, consider an equilateral spherical triangle with sides of 60 km on a spherical Earth of radius 6371 km; the side corresponds to an angular distance of 60/6371=.0094, or approximately 10 −2 radians (subtending an angle of 0.57
An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.