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, it was shown that a generalized integral of order one for each non-negative integer k can be suitably defined to reduce James' formulas to the usual form, where the coefficients are more complicated than the usual Euler-Fourier form.
Abstract: Abstract In considering a problem on certain summable (C, k) trigonometric series, R. D. James [13] used a symmetric pk+2- integral defined earlier to recapture the coefficients of the series from the sum function. James' formulas for the coefficients are more complicated than the usual Euler-Fourier form since the pk + 2 - integral is of order k + 2. It is shown that a generalized integral of order one for each non-negative integer k can be suitably defined to reduce James' formulas to the usual form.
1 citations
Patent•
09 Jun 2005
TL;DR: In this article, a phase difference calculating circuit for high precision phase control in which the table size of a memory circuit for storing an inverse trigonometric function and the circuit scale associated with that can be reduced is presented.
Abstract: PROBLEM TO BE SOLVED: To provide a phase difference calculating circuit for use in high precision phase control in which the table size of a memory circuit for storing an inverse trigonometric function and the circuit scale associated with that can be reduced SOLUTION: A sequential signal processing circuit 102 calculates a phase rotation amount w (t) by LMS algorithm, and a real part output circuit 103 calculates the real part W r (t) of the w (t) An ROM 104 searches a phase θ based on the real part W r (t) and a table of arc cosine inverse trigonometric function storing 0-π rad A code determination circuit 105 determines the code data of the imaginary part w i (t) of the w (t) and a phase angle correcting circuit 106 corrects the phase θ based on the code data thus obtaining a desired phase difference θ r COPYRIGHT: (C)2005,JPO&NCIPI
1 citations
Posted Content•
TL;DR: This article modified the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, and basing these functions independently on Eisenstein function $\varepsilon_2$.
Abstract: We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $\varepsilon_2$.
1 citations
TL;DR: The Lorentz triangle search variable step coefficient was proposed based on the broad-spectrum trigonometric functions combined with the LorentZ chaotic mapping strategy to improve the global search ability and local development ability of the AOA.
Abstract: With the increasing complexity and difficulty of numerical optimization problems in the real world, many efficient meta-heuristic optimization methods have been proposed to solve these problems. The arithmetic optimization algorithm (AOA) design is inspired by the distribution behavior of the main arithmetic operators in mathematics, including multiplication (M), division (D), subtraction (S) and addition (A). In order to improve the global search ability and local development ability of the AOA, the Lorentz triangle search variable step coefficient was proposed based on the broad-spectrum trigonometric functions combined with the Lorentz chaotic mapping strategy, which include a total of 24 search functions in four categories, such as regular trigonometric functions, inverse trigonometric functions, hyperbolic trigonometric functions, and inverse hyperbolic trigonometric functions. The position update was used to improve the convergence speed and accuracy of the algorithm. Through test experiments on benchmark functions and comparison with other well-known meta-heuristic algorithms, the superiority of the proposed improved AOA was proved.
1 citations
Patent•
16 Oct 1996
TL;DR: In this article, the authors propose a teaching tool for helping study mathematics, comprising a frame whose middle is provided with a round hole, a transparent disc (or a ring) and an opaque disc.
Abstract: The utility model discloses a teaching tool for helping study mathematics, comprising a frame whose middle is provided with a round hole, a transparent disc (or a ring) and an opaque disc. The overall thickness of two discs is identical with the thickness of the frame. After the two discs are superposed and placed in the frame, the two discs can be rotated flexibly without interference. Each part is marked with centimeter scales, or a plurality of kinds of logarithmic linear groups, or trigonometric function linear groups, or 100 or 360 equidistant lattices, or abscissa, or ordinate or mathematic symbols. Various correlations among provided conditions and the rotation of the discs are used. The utility model can be used for calculating positive and inverse trigonometric functions, logarithm, equation and rational number, drawing various geometrical figures and helping remember triangular formulas.
1 citations