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In the present investigation, a study of the non-experimental or expost-facto type has been carried out. This type of research is carried out without manipulating the variables. With this in mind, our research will not intentionally vary the independent variables. As the research is non-experimental, the phenomena are observed as they occur (naturally), in order to finally analyze them and obtain conclusions for the research.The subject under investigation is the discipline of Spherical Trigonometry, analyzing its study in the Universities belonging to the Council of Rectors of Chile (CRUCH) in the V region.For this purpose, a didactic and methodological proposal has been elaborated and designed, through the guide text Spherical Trigonometry. This proposal will be applied to the Pedagogy of Mathematics and Computer Science and Pedagogy in Mathematics Career at the Playa Ancha University of Educational Sciences, in order to measure whether significant learning is generated in this group, outlined in the proposed objective.Generating the application and measuring the results obtained, we can say that the objective of generating the expected learning is fulfilled.