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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TL;DR: In this paper, the power series quotient monotone rule is used to prove Shafer-Fink inequalities for the inverse sine to arc hyperbolic sine.
Abstract: In this paper, we extend some Shafer-Fink-type inequalities for the inverse sine to arc hyperbolic sine, and give two simple proofs of these inequalities by using the power series quotient monotone rule.
27 citations
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TL;DR: In this paper, the Nikol'skii class of functions and generalized Lipschitz class were studied for sums of trigonometric series with positive and general monotone coefficients.
Abstract: We study when sums of trigonometric series belong to given function classes. For this purpose we describe the Nikol’skii class of functions and, in particular, the generalized Lipschitz class. Results for series with positive and general monotone coefficients are presented.
27 citations
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TL;DR: This paper established Wilker-and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions and provided a laconic proof to Oppenheim's problem associated with inequalities involving the sine and cosine functions.
Abstract: We establish Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions. We also provide a laconic proof to Oppenheim’s problem associated with inequalities involving the sine and cosine functions.
26 citations
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TL;DR: A robust technique for the single-phase grid voltage fundamental amplitude, frequency, and phase angle estimation under distorted grid conditions based on a demodulation method tuned at a fixed frequency, which is less affected by dc offset, can provide faster frequency estimation, and also avoids interdependent loop, trigonometric, and inverse trig onometric functions operation.
Abstract: This paper proposes a robust technique for the single-phase grid voltage fundamental amplitude, frequency, and phase angle estimation under distorted grid conditions. It is based on a demodulation method tuned at a fixed frequency. It does not have stability issue due to an open-loop structure, does not require real-time evaluation of trigonometric and inverse trigonometric functions, and also avoids the use of look-up table. It can provide accurate estimation of the single-phase grid voltage fundamental parameters under dc offset and harmonics. When compared with a frequency adaptive demodulation technique, the proposed one is less affected by dc offset, can provide faster frequency estimation, and also avoids interdependent loop, trigonometric, and inverse trigonometric functions operation. Simulation and experimental results are presented to verify the performance of the proposed technique.
26 citations
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23 Jan 2011
TL;DR: In this paper, a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms, polylogarithm, direct and inverse trigonometric functions, algebraic and hypergeometric functions as well as functions defined by integrals, such as the Gaussian error function.
Abstract: The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/π = 0.63661, which is the experiment's probability of success. Generalizing the experiment and simplifying the computational framework, we consider probability distributions, which can be produced perfectly, from a discrete source of unbiased coin flips. We describe and analyse a few simple Buffon machines that generate geometric, Poisson, and logarithmic-series distributions. We provide human-accessible Buffon machines, which require a dozen coin flips or less, on average, and produce experiments whose probabilities of success are expressible in terms of numbers such as π, exp(−1), log2, √3, cos(1/4), ζ(5). Generally, we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms, polylogarithms, direct and inverse trigonometric functions, algebraic and hypergeometric functions, as well as functions defined by integrals, such as the Gaussian error function.
26 citations