One of the primary applications of trigonometry was navigation, and certain commonly used navigational formulas are stated most simply in terms of these archaic function names. The haversine formula is a re-formulation of the spherical law of cosines, but the formulation in terms of haversines is more useful for small angles and distances. The haversine formula is a very accurate way of computing distances between two points on the surface of a sphere using the latitude and longitude of the two points. All of these can be expressed simply in terms of the more familiar trigonometric functions. The additional trigonometric functions are versine, haversine, coversine, hacoversine, exsecant, and excosecant. The angle between two lines is the angle between the planes of the corresponding great circles.ĭid you know that there are more than the 3 trigonometric functions we are all familiar with sine, cosine and, tangent? These additional trigonometric functions are now obsolete, however, in the past, they were worth naming.Straight lines are great circles, so any two lines meet in two points.Some rules found in spherical geometry include: These spherical polygons are defined by a number of intersecting great circles on a sphere. Spherical geometry considers spherical trigonometry which deals with relationships between trigonometric functions to calculate the sides and angles of spherical polygons. Therefore, calculating distances on a sphere needs to consider spherical geometry, the study of shapes on the surface of a sphere. But, even though the circumference of the Earth is about 40,000 kilometers, flat-Earth formulas for calculating the distance between two points start showing noticeable errors when the distance is more than about 20 kilometers. The Earth is round but big, so we can consider it flat for short distances. You can find our more on geodesic distances from the previous blog (. I decided to look into some of the mathematics that makes it possible to calculate distances considering 3D space, for example, calculating distance on a sphere.
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