From ratios of right triangle to unit circle: an introduction to trigonometric functions

Abstract

Knowing the two contexts of trigonometry both trigonometry as ratios of right-angle triangle and trigonometry as a function is important to students. Educational research has shown that students could not distingush between these contexts and understand why trigonometry is a function. Study showed that a unit circle context can be a ‘glue’ between them. However, the transition from the triangle concept to unit circle concept is not well delivered. In this study we propose a lesson design for trigonometric to filling the gap between right triangle context and circular function context. This study is underpinned by the previous research proposed by Altman & Kidron (2017) that describe how is students cognitive process through constructing knowlegde. We also report on the results of a classroom case study in which the design has been implemented and researched through a phenomenological investigation based on interviews, classroom observations. We discuss the task-related difficulties that students faced in their concept development. The results of the study suggest that the design can link between trigonometry as ratios of right-angle triangle context and unit circle context. A consideration of technical support in group work devision is also discussed.