The Transition from Ratios to Trigonometric Functions

Abstract Our motivation comes from the difficulties that appeared in the lessons involving trigonometric functions, related to the trigonometric circle and the measure of an angle in radians. The aim was to investigate the contributions of an approach combining constructions with a dynamic software and concrete material. Based on the Meaningful Learning Theory, we chose subsumed concepts related to the definition of the sinus function and applied a set of activities for nine students from a teachers Course in Mathematics, using the Design Based Research. For drawing up the activities, we considered historical development of concepts of trigonometry and recommendations from the Brazilian National Curriculum Standards. Our intervention was not enough for the participants to achieve a significant learning in trigonometry. However, we observed that everyone managed to build a table and a graph of a periodic function, and two participants were able to sketch the graph of the sinus function.