<![CDATA[Understanding trigonometric functions at angles beyond 90 degrees presents unique cognitive challenges for students, requiring the integration of conceptual, procedural, and representational knowledge. However, research exploring how students cognitively process such problems, especially within a structured framework, remains limited. This study aims to analyze students’ cognitive processes in solving trigonometric problems involving beyond-90-degree angles through the DAPIC framework (Define, Assess, Plan, Implement, Communicate), offering a novel application of DAPIC to this underexplored context. A qualitative case study approach was employed, involving six 11th-grade students from a public high school with varying cognitive levels. Data were collected through diagnostic tasks, think-aloud protocols, and semi-structured interviews, and were analyzed by mapping students’ thinking patterns, defined as the recurring sequences of cognitive moves and representation use observed across DAPIC stages. The results reveal that high-performing students demonstrated flexible shifts between symbolic, graphical, and unit circle representations and were capable of self-regulating their errors reflectively. In contrast, students with moderate and low performance encountered difficulties in identifying the quadrant of angles and understanding the periodic nature of trigonometric functions, particularly during the Assess and Plan stages. Adaptive strategies, such as visual re-checking or intuitive quadrant reasoning, emerged spontaneously but were not always effective. These findings suggest that DAPIC serves as a systematic tool for capturing the dynamics of students’ thinking processes and offers valuable insights for developing deeper instructional strategies in trigonometry, especially for topics involving beyond-90-degree angles.]]>
