Inequalities related to certain inverse trigonometric and inverse hyperbolic functions [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020 A sharp double inequality between the inverse tangent and inverse hyperbolic sine functions is proved. A lower bound of $(\operatorname{arctanh} x)^2$ is given. The numerical values are calculated by CAS MAPLE.
Chao-Ping Chen, Branko Malešević
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Sharp Wilker and Huygens type inequalities for trigonometric and inverse trigonometric functions [PDF]
Journal of Mathematical Inequalities, 2020 Summary: In this paper, we prove Wilker and Huygens type inequalities for inverse trigonometric functions. This solves two conjectures proposed by the second author [Integral Transforms Spec. Funct. 23, No. 12, 865--873 (2012; Zbl 1264.26018)]. Also, we present new sharp Wilker and Huygens type inequalities for trigonometric functions.
Bo Zhang, Chao-Ping Chen
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Inverse Trigonometric Functions Arctan and Arccot [PDF]
Formalized Mathematics, 2008 Summary. This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several dierentiation formulas of arctan and arccot.
Xiquan Liang, Bing Xie
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Time Dependent Inverse Optimal Control using Trigonometric Basis Functions [PDF]
Conference on Learning for Dynamics & Control, 2023 The choice of objective is critical for the performance of an optimal controller. When control requirements vary during operation, e.g. due to changes in the environment with which the system is interacting, these variations should be reflected in the ...
Rahel Rickenbach +2 more
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An Implementation of Inverse Cosine Hardware for Sound Rendering Applications [PDF]
Sensors, 2023 Sound rendering is the process of determining the sound propagation path from an audio source to a listener and generating 3D sound based on it. This task demands complex calculations, including trigonometric functions. This paper presents hardware-based
Jinyoung Lee +3 more
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A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions [PDF]
, 2017 In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.
Branko Malešević +2 more
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Inverse spherical Bessel functions generalize Lambert W and solve similar equations containing trigonometric or hyperbolic subexpressions or their inverses [PDF]
Maple Transactions, 2022 A strict integer Laurent polynomial in a variable x is 0 or a sum of one or more terms having integer coefficients times x raised to a negative integer exponent. Equations that can be transformed to certain such polynomials times exp(-x) = constant are
David Stoutemyer
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Addition formulas of leaf functions according to integral root of polynomial based on analogies of inverse trigonometric functions and inverse lemniscate functions [PDF]
, 2017 The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differential equation is constructed.
Kazunori Shinohara
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Inverse Trigonometric Functions Arcsec and Arccosec [PDF]
Formalized Mathematics, 2008 The papers [1], [2], [16], [3], [12], [17], [13], [5], [8], [11], [14], [4], [6], [7], [10], [15], and [9] provide the notation and terminology for this paper. In this paper x, r denote real numbers. The following propositions are true: (1) [0, π2 [⊆ dom (the function sec). (2) ]π2 , π] ⊆ dom (the function sec). (3) [−π2 , 0[⊆ dom (the function cosec).
Bing Xie, Xiquan Liang, Fuguo Ge
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Inequality chains related to trigonometric and hyperbolic functions and inverse trigonometric and hyperbolic functions [PDF]
Journal of Mathematical Inequalities, 2013 Wepresent inequality chains related to trigonometric and hyperbolic and inverse trigono- metric and hyperbolic functions.
Chao-Ping Chen, József Sándor
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