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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07 Apr 2023
TL;DR: In this article , the authors discuss the work of a brilliant line of Mathematicians who lived in central Kerala and starting with its founder Madhava (1350 CE) developed what can best be described as Calculus and applied it to a class of trigonometric functions.
Abstract: We discuss the work of a brilliant line of Mathematicians who lived in central Kerala and starting with its founder Madhava (1350 CE) developed what can best be described as Calculus and applied it to a class of trigonometric functions. We explain, with the example of the expansion of the inverse tan function, how they handled integration. Further, they took forward the work of the fifth century mathematician Aryabahata (499 CE), worked with differentials, and developed the expansion of the sine and the cosine functions. The work \textit{Yuktibhasa} (circa 1500 CE) which maybe described as the first textbook on Calculus, also describes in detail the evaluation of the area and volume of trigonometric functions as well as a variety of expansions for $\textit{pi}$. Our treatment is pedagogical and we present exercise problems and invite the enterprising student to try their hands at approximations and integration $\textit{a la}$ the Madhava way.
15 May 2022
TL;DR: In this paper , the authors proposed a method to improve the accuracy of parameter estimation for the magnetic flux saturation model of a synchronous reluctance motor. But this method requires the current and flux to be measured and calculated during hysteresis voltage injection test.
Abstract: This paper proposes a method to improve the accuracy of parameter estimation for the magnetic flux saturation model of a synchronous reluctance motor. The selected flux saturation model includes an arctangent function representing the nonlinear relationship between current and flux. The parameter estimation algorithm integrates the arctangent model with respect to current and transforms the model into a polynomial to which Least Squares Method (LSM) can be applied. For the estimation, measured currents and calculated flux are used and obtained during hysteresis voltage injection test. Because the locus of the current and flux shows the hysteresis band, estimation errors may occur when using the integral. This paper proposed an initialization method for each integration interval to mitigate the error caused by the hysteresis band. The proposed method was validated on an experimental set of 1.5 kW SynRM.
15 Mar 2022
TL;DR: In this article , a cyclic function is determined to correspond as the equivalent of the classic sine formula to isosceles triangles, which is called isn^-1(x) sine equivalent.
Abstract: Abstract This paper discusses a new formula to solve for the angle of isosceles triangles given proportion of differentiated unequivalent edge length versus the always-equivalent edges. The equation is equal to the arcsine of (X/2) multiplied by two. This formula is to be called ‘isn^-1(x)’, short for inverse isosceles sine equivalent. Also discussed is the non-inverse ‘isn(x)’ which is the cyclic function which is determined to correspond as the equivalent of the classic sine formula to isosceles triangles. The formula set is clearly superior and powerful at calculating the angle and measure of any given obtuse or acute triangle of an unclassified type, as well as unifying a simplest-fit formula across all types of triangle.
01 Jan 2023
TL;DR: In this paper , an arctangent least mean square/fourth algorithm was developed by incorporating the standard least-means-square-fourth algorithm cost function with the arctagonent framework for adaptive system identification.
Abstract: This work proposes an arctangent least mean square/fourth algorithm developed by incorporating the standard least mean square/fourth algorithm cost function with the arctangent framework for adaptive system identification. The performance of the proposed algorithm is verified through various simulations which shows that the proposed algorithm outperforms the conventional least mean square/fourth algorithm.