3D Visualization and Integration of Trigonometric Functions in MATLAB: A Dynamic Learning Object and Simulation
Abstract
This study presents a MATLAB-based computational framework for the three-dimensional visualization and numerical double integral analysis of trigonometric functions. The proposed system integrates symbolic function representation, numerical computation, dynamic surface generation, and graphical rendering within a unified computational environment. A trigonometric surface model was constructed and analyzed using structured numerical grids and real-time visualization procedures. In addition to the original trigonometric surface, a numerical double integral surface was generated to examine accumulation behavior across the computational domain. The developed framework enables dynamic observation of oscillatory surface structures, multidimensional variation patterns, and integration-based geometric transformations. The obtained results demonstrate that the proposed system successfully produces stable graphical representations and numerically consistent integral surfaces without computational discontinuities. Comparative analysis between the original trigonometric surface and its corresponding integral representation reveals the transformation from periodic oscillatory behavior to cumulative accumulation structures. Unlike conventional static mathematical demonstrations, the proposed framework combines numerical integration and interactive three-dimensional visualization within a reproducible MATLAB environment. The contribution of the study is primarily computational and methodological, providing a reproducible visualization framework for the exploratory analysis of multivariable trigonometric systems and numerical integration behavior.
Keywords
MATLAB, Trigonometric Functions, Trigonometric Functions, Learning Objects, E-Learning, Mathematical Modeling
Supporting Institution
Project Number
Ethical Statement
Thanks
References
- V. Naicker, “Educator's pedagogy influencing the effective use of computers for teaching purposes in classrooms: Lessons learned from secondary schools in South Africa”, Educational Research and Reviews, vol. 5, no. 11, pp. 674–689, 2010.
- T. Öztürk, Matematik öğretiminde bilgisayar destekli öğretim yöntemiyle hazırlanan animasyon tekniğinin kullanımı, 2011.
- K. Salas and L. Ellis, “The development and implementation of learning objects in a higher education setting”, Interdisciplinary Journal of Knowledge and Learning Objects, vol. 2, pp. 1–19, 2006.
- B. J. Walker, A. K. Townsend, A. K. Chudasama, and A. L. Krause, “VisualPDE: Rapid interactive simulations of partial differential equations”, Bulletin of Mathematical Biology, vol. 85, p. 113, 2023.
- E. Ekmez, “Deneysel doğrulamadan formel ispata uzanan süreçte dinamik geometri yazılımlarının potansiyeli”, Turkish Journal of Computer and Mathematics Education, vol. 7, no. 1, pp. 24–34, 2016.
- B. Özçakır, “The effects of mathematics instruction supported by dynamic geometry activities on seventh grade students’ achievement in area of quadrilaterals”, Yüksek lisans tezi, Orta Doğu Teknik Üniversitesi, 2013.
- L. Pinter and M. F. H. Siddiqui, “Enhancing calculus learning through interactive VR and AR technologies: A study on immersive educational tools”, Multimodal Technologies and Interaction, vol. 8, no. 3, p. 19, 2024.
- R. H. Kay and L. Knaack, “Evaluating the learning in learning objects,” Open Learning, vol. 22, no. 1, pp. 5–28, 2007.
- R. H. Kay and L. Knaack, “Investigating the use of learning objects in secondary school mathematics”, Interdisciplinary Journal of E-Learning and Learning Objects, vol. 4, 2008.
- Schoenherr, J., Strohmaier, A. R., & Schukajlow, S. Learning with visualizations helps: A meta-analysis of visualization interventions in mathematics education. Educational Research Review, 45, 100639, 2024.