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    Trigonometria Esférica: origens e aplicações
    (Universidade Federal de São Paulo (UNIFESP), 2020-02-28) Faria, Jorge Maurilio De [UNIFESP]; Moraes, Rodolpho Vilhena De [UNIFESP]; Universidade Federal de São Paulo
    The present work aims to carry out a historical study of Spherical Trigonometry, covering since its origins and purposes, as well as applications in daily life and its relationship with Astronomy. Also take a trip on the national curriculum to observe how the theme is inserted in the school grid. I highlight here the works of (USUI, 2014) , which inspired me with some contribution in the development of my research, in which I was able to deepen the questions about the coordinate transformations. The elements of Spherical Trigonometry are presented through definitions and theorems. We present the fundamental relation, known as the relation of the four elements (Law of the Cosines) and the Law of the Sines, the Celestial Sphere, its elements and its coordinates in the equatorial system, horizontal system and hourly system. Also present the triangle of position as being a spherical triangle, relating the coordinates of different systems of a star. From the studies carried out, we present a didactic sequence, allowing the calculation of distances between two distinct stars in the Celestial Sphere, involving Spherical Geometry, Spherical Trigonometry and the Celestial Sphere, especially the distance between cities on our planet. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Financial Code 001.