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Abstract
This article analyzes the methodological potential of a multiple-representation approach based on visual and illustrative modeling in teaching the fundamental concepts of trigonometry. During the learning process, students frequently experience difficulties in understanding the intrinsic relationships among the unit circle, right triangles, and the graphs of trigonometric functions. To address these challenges, the study proposes an alternative model for constructing the trigonometric circle. The proposed model aims to reveal the logical origins of trigonometric concepts, support their spatial and intuitive perception, and establish a holistic connection among the unit circle, graphical representations, and geometric models. The article examines the solution of trigonometric inequalities as an instructional example by employing various visual and analytical methods and provides a rationale for their didactic effectiveness. The impact of this approach on the efficiency of learning trigonometry was evaluated with 94 final-year high school students from two selected public schools in Uzbekistan (45 in the control group and 49 in the experimental group). A mixed-methods research design was adopted, integrating quantitative data obtained from student assessments with qualitative data collected through interviews. The findings indicate that students’ abilities to analyze problems, justify solutions, and make generalizations were significantly improved.
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article Type: Research Article
EURASIA J Math Sci Tech Ed, Volume 22, Issue 4, April 2026, Article No: em2821
https://doi.org/10.29333/ejmste/18332
Publication date: 08 Apr 2026
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