Modeling real-world periodic phenomena using sine and cosine functions
DOI:
https://doi.org/10.64171/JAES.6.4.26-30Keywords:
Sine function, Cosine function, Periodic phenomena, Mathematical modeling, TrigonometryAbstract
This investigation examined the effectiveness of sine and cosine functions in modeling real-world periodic phenomena. A dataset exhibiting a repeating pattern over a 12-month cycle was analyzed to determine the amplitude, midline, period, and frequency coefficient needed to construct an appropriate sinusoidal model. The developed cosine function was compared with the observed data to evaluate its accuracy using residual errors and the Mean Absolute Error (MAE). Results showed that the model accurately represented the periodic behavior of the selected phenomenon, with predicted values matching the observed values and an MAE of zero, indicating a perfect fit for the sample dataset. The findings demonstrate that sine and cosine functions are reliable mathematical tools for describing and predicting recurring patterns. This investigation also highlights the practical applications of trigonometric modeling in mathematics, science, engineering, and environmental studies while reinforcing students' understanding of mathematical modeling and the analysis of periodic phenomena.
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Copyright (c) 2026 Jonalyn DG. Figueroa, Lorraine A. Yuson, Jester Lee S. Hipol, Mark Ren D. Villaflor, Titin Rahmiatin Rahim, Usman
This work is licensed under a Creative Commons Attribution 4.0 International License.