DERIVATION OF FUNDAMENTAL TRIGONOMETRIC IDENTITIES

Authors

  • Otajonova Sitorabonu Shuxratovna Asia International University Trainee Teacher, Department of General Technical Sciences

DOI:

https://doi.org/10.55640/

Keywords:

Trigonometry, trigonometric identities, sine, cosine, tangent, cotangent, unit circle, Pythagorean identity, angle-sum formulas, trigonometric rule, proof, analytic geometry, function theory, geometry, mathematical logic.

Abstract

In this article, the step-by-step derivation of the fundamental trigonometric identities is analyzed. Trigonometry is one of the most essential branches of mathematics and has significant practical applications in fields such as geometry, physics, engineering, and computer graphics. By examining the relationships among the identities, the geometric meaning of the sine, cosine, tangent, and cotangent functions, and the fundamental connections between the trigonometric ratios of an angle, the main formulas are proven. The article also discusses the derivation of identities using the unit-circle approach, similarity principles, the Pythagorean theorem, sum and difference formulas, even-odd properties, and trigonometric expressions involving products and sums. The results of the study provide a deeper understanding of how the fundamental formulas—widely applied in trigonometric equations, analytic geometry, and the theory of functions—are derived.   

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References

1.Otajonova, S. S. (2025). INTERACTIVE METHODS IN TEACHING MATHEMATICS TO PRIMARY SCHOOL STUDENTS: FOSTERING ENGAGEMENT AND CONCEPTUAL UNDERSTANDING. PEDAGOGIK TADQIQOTLAR JURNALI, 2(2), 84-87.

2.Otajonova , S. (2024). APPLICATION OF ELEMENTS OF TRIGONOMETRY IN SOLUTION OF TRIANGLES. Medicine, Pedagogy and Technology: Theory and Practice, 2(9), 292–304. Retrieved from

3.Shukhratovna, O. S. (2025). ORGANIZING INTERESTING GAMES FOR ELEMENTARY GRADES USING ELEMENTS OF COMBINATORICS. PEDAGOGIK TADQIQOTLAR JURNALI, 3(2), 117-119.

4.Shukhratovna, O. S. (2025). THE ROLE OF ARITHMETIC PROGRESSIONS IN LIFE PROCESSES. PEDAGOGIK TADQIQOTLAR JURNALI, 3(1), 351-354.

5.Otajonova S. . (2025). MATEMATIK KREATIVLIKNI O‘QITISHDA GAMIFIKATSIYA VA INTERAKTIV O‘YINLARDAN FOYDALANISH . Development Of Science, 5(1), pp. 56-64. https://doi.org/0

6.Shuxratovna, O. S. BOSHLANG‘ICH SINFLAR UCHUN MATEMATIKA FANINI QIZIQARLI O ‘QITISH METODIKASI.

7.Shuxratovna, O. S. O‘QITUVCHILARNING KASBIY RIVOJLANISHIGA DOIR PEDAGOGIK SEMINARLAR VA TRENINGLAR.

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Published

2025-12-05

Issue

Vol. 4 No. 11 (2025): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

DERIVATION OF FUNDAMENTAL TRIGONOMETRIC IDENTITIES. (2025). Journal of Multidisciplinary Sciences and Innovations, 4(11), 294-298. https://doi.org/10.55640/

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