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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 2 • Issue 1 • PP: 33-43 • 2022

A Study in the Integral of Sine and Cosine Functions

Maissam Jdid 1*
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,
Fatima Al Suleiman 2
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1Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria
2Business Supervisor, Department of Mathematical, Faculty of Science, Damascus, Syria
* Corresponding Author.
DOI https://doi.org/10.54216/GJMSA.020105
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Received: March 22, 2022 Accepted: July 27, 2022
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Abstract

Trigonometric functions are among the most widely used functions in many science fields, especially sine and cosine functions because they are essential for periodic functions that describe sound and light waves in different types and wavelengths. Therefore, researchers studied the integrals of sine and cosine functions in different forms of the integrating function. In this paper, we spotlighted several most important yet under-studied integrals that are poorly mentioned in Arabic and foreign textbooks and studies. In addition, we studied Integral of Sine and Cosine for n as a positive rational number and concluded that each of these integrals leads to functional series. When studying the convergence of these series using the D'Alembert ratio test, we found that these series are convergent over the entire set of real numbers. This convergence is highly useful when applying such integrals in different science fields.

Keywords

Power Series Sine Cosine Convergence Integral D'Alembert Ratio Test.

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Jdid, Maissam, Suleiman, Fatima Al. "A Study in the Integral of Sine and Cosine Functions." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 2, no. Issue 1, 2022, pp. 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
Jdid, M., Suleiman, F. (2022). A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications, Volume 2(Issue 1), 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
Jdid, Maissam, Suleiman, Fatima Al. "A Study in the Integral of Sine and Cosine Functions." Galoitica: Journal of Mathematical Structures and Applications Volume 2, no. Issue 1 (2022): 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
Jdid, M., Suleiman, F. (2022) 'A Study in the Integral of Sine and Cosine Functions', Galoitica: Journal of Mathematical Structures and Applications, Volume 2(Issue 1), pp. 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
Jdid M, Suleiman F. A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications. 2022;Volume 2(Issue 1):33-43. DOI: https://doi.org/10.54216/GJMSA.020105
M. Jdid, F. Suleiman, "A Study in the Integral of Sine and Cosine Functions," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 2, no. Issue 1, pp. 33-43, 2022. DOI: https://doi.org/10.54216/GJMSA.020105
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