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: The Schröder's process is extended to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation and is illustrated by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number.
Abstract: Based on the Taylor's expansion of an inverse function, we extend the Schroder's process to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation. We illustrate the extended processes by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number. IFs for inverse trigonometric function evaluations are also considered.
1 citations
TL;DR: In this article , two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions were established and applied to obtain some refinement and extension of Mitrinović-Adamović and Lazarević inequalities.
Abstract: In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities. The inequalities obtained in this paper go beyond the conclusions and conjectures in the previous literature. Finally, we apply the main results of this paper to the field of mean value inequality and obtain two new inequalities on Seiffert-like means and classical means.
1 citations
TL;DR: In this article , the authors established a general inequality for the hyperbolic functions, extended the newly established inequality to trigonometric functions, and obtained some new inequalities involving the inverse sine and inverse Hyperbolic sine functions, applying these inequalities to the Neuman-Sándor mean and the first Seiffert mean.
Abstract: In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean.
1 citations
Patent•
01 Apr 2004
TL;DR: In this article, a kind of method for analyzing dual sine wave signal angle is disclosed, which includes the following steps: converting the analog signal values of the first sines wave and the second sineswave into the digital signal values; performing normalization onto the digital signals of the Sine Wave and the Second Sine wave to obtain the first normalization value and the two normalization values; obtaining the inverse cosine values of both the SINR values; and adding the variation values per unit cycle to the cycle number; and finally, converting the first SIN
Abstract: A kind of method for analyzing dual sine wave signal angle is disclosed in the present invention. The dual sine waves are the first sine wave and the second sine wave, respectively. The invention includes the following steps: converting the analog signal values of the first sine wave and the second sine wave into the digital signal values; performing normalization onto the digital signal values of the first sine wave and the second sine wave to obtain the first normalization value and the second normalization value; obtaining the inverse cosine values of the first normalization value and the second normalization value to calculate the variation values per unit cycle for the first angle and the second angle, respectively; converting the first sine wave and the second sine wave into the first square wave and the second square wave to calculate the cycle number of the first square wave and the second square wave; and adding the variation values per unit cycle to the cycle number.
1 citations