Paper Details

Name: Kotade Priyanka V.
Country: India

Year: 2026
Volume: Volume-13, Issue-1 (January-June)
Page Number: 50-61
DOI: https://doi.org/10.5281/zenodo.18654530

ABSTRACT
Trigonometry is the mathematical study of relationships between angles and lengths, originally motivated by problems in astronomy, surveying, and geometry. Over time it evolved into a central language of periodicity and rotation, deeply embedded in calculus, linear algebra, complex analysis, signal processing, physics, and modern computing. This article presents a
detailed research-style exposition of trigonometry, beginning with classical Euclidean definitions and moving through identities, inverse functions, laws of triangles, and analytic formulations. It then develops the deeper structural view of trigonometric functions as coordinate projections on the unit circle, as solutions to differential equations, and as manifestations of complex exponentials. Finally, it surveys major applications including waves,
Fourier analysis, navigation, robotics, and imaging, while highlighting contemporary computational perspectives.

Keywords: Trigonometry, Unit Circle, Angle Measurement, Trigonometric Identities, Inverse Trigonometric Functions, Laws of Sines and Cosines, Complex Exponentials, Euler’s Formula, Differential Equations, Harmonic Motion, Waves and Oscillations, Fourier Series.