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Title

A Study in the Integral of Sine and Cosine Functions

  Maissam Jdid 1 * ,   Fatima Al Suleiman 2

1  Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria
    (m.j.foit@aspu.edu.sy)

2  Business Supervisor, Department of Mathematical, Faculty of Science, Damascus, Syria
    (fatimasuliman2009@gmail.com)

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Doi   :   https://doi.org/10.54216/GJMSA.020105

Received: March 22, 2022 Accepted: July 27, 2022

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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Cite this Article as :
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MLA Maissam Jdid, Fatima Al Suleiman. "A Study in the Integral of Sine and Cosine Functions." Galoitica: Journal of Mathematical Structures and Applications, Vol. 2, No. 1, 2022 ,PP. 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
APA Maissam Jdid, Fatima Al Suleiman. (2022). A Study in the Integral of Sine and Cosine Functions. Journal of Galoitica: Journal of Mathematical Structures and Applications, 2 ( 1 ), 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
Chicago Maissam Jdid, Fatima Al Suleiman. "A Study in the Integral of Sine and Cosine Functions." Journal of Galoitica: Journal of Mathematical Structures and Applications, 2 no. 1 (2022): 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
Harvard Maissam Jdid, Fatima Al Suleiman. (2022). A Study in the Integral of Sine and Cosine Functions. Journal of Galoitica: Journal of Mathematical Structures and Applications, 2 ( 1 ), 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
Vancouver Maissam Jdid, Fatima Al Suleiman. A Study in the Integral of Sine and Cosine Functions. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2022); 2 ( 1 ): 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
IEEE Maissam Jdid, Fatima Al Suleiman, A Study in the Integral of Sine and Cosine Functions, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 2 , No. 1 , (2022) : 33-43 (Doi   :  https://doi.org/10.54216/GJMSA.020105)
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