Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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11 citations
TL;DR: A fundamental frequency estimation technique for three-phase voltage systems under unbalanced and harmonic conditions based on the Clarke transformation, recursive discrete Fourier transform, and Teager energy operator is proposed, suitable for low-cost applications.
Abstract: This article proposes a fundamental frequency estimation technique for three-phase voltage systems under unbalanced and harmonic conditions. It is based on the Clarke transformation, recursive discrete Fourier transform, and Teager energy operator. The proposed technique is computationally efficient and relatively simple to implement, thus suitable for low-cost applications. It does not require real-time evaluation of the computationally demanding inverse trigonometric functions. The proposed method does not suffer from the accumulation error and is also not affected when the voltage signal is sampled at zero or close to zero. It is immune to various voltage harmonics and can produce quick transient response with a time of less than 75% of one fundamental period. When compared with the competing techniques based on phase-locked loops and three consecutive samples, the proposed method can produce faster response under dynamic conditions. The advantages of the proposed technique are confirmed by simulated and experimental results in the laboratory.
11 citations
Posted Content•
TL;DR: In this article, various miscellaneous functional inequalities for generalized inverse trigonometric and hyperbolic functions are derived for sums, difference, and quotient functions, as well as Grunbaum inequalities with the aid of Bernoulli inequalities.
Abstract: Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.
11 citations
Book•
01 Jan 1976
TL;DR: Inverse trigonometric functions have also been used in the context of trigonometric functions as discussed by the authors, including right triangle ratio and right triangle triangulation, in the plane geometry domain.
Abstract: Right Triangle Ratios. Trigonometric Functions. Graphing Trigonometric Functions. Identities. Inverse Trigonometric Functions Trigonometric Equations and Inequalities. Additional Topics: Triangles and Vectors. Polar Coordinates Complex Numbers. Appendix A: Comments on Numbers. Appendix B: Functions and Inverse Functions. Appendix C: Plane Geometry: Some Useful Facts. Selected Answers. Index.
11 citations
TL;DR: In this article, Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions are presented for the Gaussian functions and for the non-Gaussian function.
Abstract: In this paper, we present Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions.
11 citations