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.

Device and method for operating inverse function

Abstract: PURPOSE:To operate an inverse function, especially, an inverse tangent function in a short time with a small storage capacity by providing a memory where function values of the function corresponding to plural variables respectively are stored together with these variables to operate the deviation CONSTITUTION:The memory where function values of the function corresponding to plural variables respectively are stored together with these variables is provided for the operation when a solution (function value) of the inverse function, especially, the inverse tangent function is obtained The function value of the function most approximating a given variable is read out from the memory, and first deviation between them is operated The function value of the function most approximating the first deviation is read out from the memory and is substituted into each separated function of a prescribed operation formula to operate the function value of the function Second deviation between the given variable and the operation result is operated; and when the operation result is smaller than a minimum value of function values of the function in the memory, the variable corresponding to the function value of the function is added to obtain the inverse function corresponding to the given variable Thus, the solution of the inverse function, especially, the inverse tangent function is accurately and quickly obtained with a high precision and a small storage capacity

Method and device for controlling horizontal orientation of aircraft

Abstract: FIELD: physics; control. ^ SUBSTANCE: invention relates to complex flight control of autopilot systems of aircraft. The method is based on measuring the value and direction of apparent and absolute linear acceleration, calculation of their differences, ratios of the differences, including the number to the value of acceleration of gravity, and inverse trigonometric functions of evaluations of pitching and banking. Subsequent comparison of these evaluations with given values allows for controlling orientation of the aircraft. The device has a vector accelerometre, subtracting unit, vector sensor of absolute linear acceleration, unit for setting value of acceleration of gravity, unit for determining orientation components and comparator unit. ^ EFFECT: design of non-redundant automatic control and monitoring systems, increased accuracy and reliability of control. ^ 6 cl, 6 dwg

Solutions of Problems: Derivatives and its Applications

Abstract: In this chapter, the problems of the fifth chapter are fully solved, in detail, step-by-step, and with different methods. The subjects include definition of derivative, differentiation formulas, product rule, quotient rule, chain rule, derivatives of trigonometric functions, derivatives of exponential, derivatives of logarithm functions, derivatives of inverse trigonometric functions, derivatives of hyperbolic functions, implicit differentiation, higher-order derivatives, logarithmic differentiation, applications of derivatives, rates of change, critical points, minimum and maximum values, and absolute extrema.

On Sharpness of Error Bounds for Single Hidden Layer Feedforward Neural Networks

Abstract: A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for univariate approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural networks with one input node perform such operations. Errors of best approximation can be expressed using moduli of smoothness of the function to be approximated (i.e., to be learned). In this context, the quantitative extension of the uniform boundedness principle indeed allows to construct counter examples that show approximation rates to be best possible. Approximation errors do not belong to the little-o class of given bounds. By choosing piecewise linear activation functions, the discussed problem becomes free knot spline approximation. Results of the present paper also hold for non-polynomial (and not piecewise defined) activation functions like inverse tangent. Based on Vapnik-Chervonenkis dimension, first results are shown for the logistic function.