# The Generalization of the cosinus theorem and analytical calculation of multi-beam interference with an arbitrary phase distribution

### Abstract

An important task of signal transmission systems is to calculate the result of the addition of oscillations analytically solved for two signals. In this paper, we obtained an analytical solution to the problem of calculating the result of adding an arbitrary number of unidirectional oscillations or signals. A formula is obtained for generalizing the cosine theorem for a triangle to the case of polygons of various configurations. Examples of calculating the parameters of polygons of various shapes are given.### References

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Glushchenko A.G., Glushchenko E.P. (2016). Method for calculating the spatial distribution of the intensity of the wave process formed by point sources. Bulletin of Science and Education, 11 (23), 6-10.

Randall D. (2016). Physics for Scientists and Engineers: A Strategic Approach with Modern Physics, Global Edition, Pearson, 1122.

Thorne Kip S., Blandford Roger D. (2016). Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics, Hardcover, 1477.

KhyfitsA.(2004). Theorem of cosines for pyramids, The College Mathematics Journal .35, No.5, 385–388.

Pickover, Clifford A. (2009). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. Sterling Publishing Company, Inc. p. 106.

Rade. L.,Westergren B.(2004). Mathematics Handbook for Science and Engineering, 5th Edition, Springer-Verlag, Berlin, 562.

Glushchenko A.G., Glushchenko E.P. (2016). Method for calculating the spatial distribution of the intensity of the wave process formed by point sources. Bulletin of Science and Education, 11 (23), 6-10.

Published

2020-12-16

How to Cite

GLUSHCHENKO, Alexandra; GLUSHCHENKO, Alexander; GLUSHCHENKO, Eugenia.
The Generalization of the cosinus theorem and analytical calculation of multi-beam interference with an arbitrary phase distribution.

**European Journal of Physics Education**, [S.l.], v. 11, n. 3, p. 38-46, dec. 2020. ISSN 1309-7202. Available at: <http://eu-journal.org/index.php/EJPE/article/view/277>. Date accessed: 22 sep. 2023.
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Section

Classroom Physics

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