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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.
5 lip 2024 · The study of the relationships between the sides and angles of triangles drawn on a sphere's surface is known as spherical trigonometry. By using trigonometric concepts in non-planar geometry, it deals with the measurement and computation of angles, distances, and areas on spherical surfaces.
To derive the basic formulas pertaining to a spherical triangle, we use plane trigonometry on planes related to the spherical triangle. For example, planes tangent to the sphere at one of the vertices of the triangle, and central planes containing one side of the triangle.
26 lis 2024 · Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere to the vertices are therefore given by a=OA^->, b=OB^->, and c=OC^->.
Spherical Trigonometry is a specialized branch of trigonometry that studies the relationships between angles and distances on the surface of a sphere. Unlike planar trigonometry, which deals with flat, two-dimensional surfaces, spherical trigonometry is concerned with spherical surfaces and the geometry inherent to them.
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 is the study of curved triangles, triangles drawn on the surface of a sphere. The subject is practical, for example, because we live on a sphere. The subject has numerous elegant and unexpected theorems.
