Calculus of Trigonometric Functions in Machine Learning Algorithms
Senior Grade Lecturer in Science, Government Polytechnic, Harapanahalli-583131, Karnataka India.
Research Article
World Journal of Advanced Research and Reviews, 2022, 15(02), 926-931
Publication history:
Received on 09 August 2022; revised on 17 August 2022; accepted on 24 August 2022
Abstract:
The calculus of trigonometric functions provides essential mathematical infrastructure for numerous machine learning algorithms, from gradient-based optimization in neural networks to frequency-domain feature extraction and periodic pattern recognition. This paper presents a comprehensive examination of how derivatives and integrals of sine, cosine, and related functions enable and enhance learning algorithms across diverse applications. We explore the theoretical foundations of trigonometric differentiation and integration, their implementation in neural network architectures through activation functions and loss formulations, their central role in Fourier-based spectral methods, and their influence on optimization dynamics in high-dimensional parameter spaces. Through detailed mathematical analysis supported by equations, tables, and figures, we demonstrate that trigonometric calculus remains indispensable for domains requiring frequency analysis, rotational invariance, and periodic structure modeling. The analysis reveals fundamental connections between classical harmonic analysis and modern deep learning, providing insights for algorithm design in specialized applications including robotics, signal processing, and physics-informed machine learning.
Keywords:
Trigonometric functions; Calculus; Machine learning algorithms; Gradient-based optimization; Loss functions; Periodic features; Nonlinear activation functions; Backpropagation; Feature transformation
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