About Cotangent
https://doi.org/10.22405/2226-8383-2023-24-5-167-179
Abstract
In this paper we describe a reasoning method which allows to get relatively simple estimates of cotangent values for angles in the half-interval (0, 𝜋/2 ]. The method is based on the ability of the cotangent to refine some of its estimates that were derived from other considerations. As an illustration of the method we give cotangent estimates for two subclasses of rational functions.
About the Author
Sergey Yurievich Soloviev
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Gelfand, I. M., Lvovsky, S. M. & Toom, A. L. 2008, Trigonometry, MCCME, Moscow, 199 p. (in Russian)
2. Gelfand, I. M., Saul M. 2001, Trigonometry, Birkh¨auser, Boston, MA, 229 p.
3. Gursky, I.P. 1968, Functions and graphs build, Prosveschenie, Moscow, 215 p. (in Russian)
4. Kaazik, Y. A. 2007, Mathematical dictionary, Fizmatlit, Moscow, 336 p. (in Russian)
5. Vinogradov, I. M. (ed.) 1982, Encyclopedia of mathematics, Sov.Entsiklopediya, Moscow, 592 p. (in Russian)
6. Shary, S.P. 2022, Course of computational methods, Novosibirsk State University, Novosibirsk, 668 p. (in Russian)
7. Bradis, V. M. 1935, Theory and practice of computing, UchPegGiz, Moscow, 280 p. (in Russian)
8. Markushevich, A. I. 1975, Recursion sequences, Mir Publishers, Moscow, 48 p. (in Russian)
9. Goloveshkin, V. A., Ulyanov, M. V. 2006, Recursion theory for programmers, Fizmatlit, Moscow, 296 p. (in Russian)
10. Sominsky, I. S. 1975 The Method of Mathematical Induction, Mir Publishers, Moscow, 63 p. (in Russian)
11. Gunderson, D. S. 2011 Handbook of mathematical induction: Theory and applications, CRC Press, Boca Ratton, FL, 893 p.
12. Ilyin, V. A., Poznyak, E. G. 2005, Basics of Mathematical Analysis (part 1), Fizmatlit, Moscow, 648 p. (in Russian)
13. Tikhonov, A. N., Vasil’eva, A. B., Sveshnikov, A. G. 1985, Differential Equations, Springer-Verlag, Berlin, 256 p.
14. Trenogin, V. A. 2002, The Functional Analysis, Fizmatlit, Moscow, 488 p. (in Russian)
15. Kudriavtsev, L. D. 2022, Course of Mathematical Analysis, vol. 2, Iurait Publ., Moscow, 720 p. (in Russian)
Review
For citations:
Soloviev S.Yu. About Cotangent. Chebyshevskii Sbornik. 2023;24(5):167-179. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-5-167-179
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