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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3 citations
Proceedings Article•
18 Jul 2021TL;DR: In this article, a finite family of activation functions called superexpressive activations is defined, where any multivariate continuous function can be approximated by a neural network that uses these activations and has a fixed architecture only depending on the number of input variables.
Abstract: We call a finite family of activation functions superexpressive if any multivariate continuous function can be approximated by a neural network that uses these activations and has a fixed architecture only depending on the number of input variables (i.e., to achieve any accuracy we only need to adjust the weights, without increasing the number of neurons). Previously, it was known that superexpressive activations exist, but their form was quite complex. We give examples of very simple superexpressive families: for example, we prove that the family {sin, arcsin} is superexpressive. We also show that most practical activations (not involving periodic functions) are not superexpressive.
3 citations
01 Jan 2014
TL;DR: The main focus of as discussed by the authors is to study the inverses of the quaternion trigonometric and hyperbolic functions, and their properties, and prove the most known facts.
Abstract: The main focus of this chapter is to study the inverses of the quaternion trigonometric and hyperbolic functions, and their properties. Since the quaternion trigonometric and hyperbolic functions are defined in terms of the quaternion exponential function e p , it can be shown that their inverses are necessarily multi-valued and can be computed via the quaternion natural logarithm function ln(p). The s facts we shall see here attest the great interest of these functions in mathematics. Proofs of the most known facts are ommited.
3 citations
TL;DR: In this article, an inverse trigonometric function generator using CMOS technology is presented and implemented, which can be used in many measurement and instrumentation systems and can achieve nonlinearity of less than 2.8% for the entire input range.
Abstract: An inverse trigonometric function generator using CMOS technology is presented and implemented. The development and synthesis of inverse trigonometric functional circuits based on the simple approximation equations are also introduced. The proposed inverse sine function generator has the infinite input range and can be used in many measurement and instrumentation systems. The nonlinearity of less than 2.8% for the entire input range of 0.5 Vp-p with a small-signal bandwidth of 3.2 MHz is achieved. The chip implemented in 0.25 μm CMOS process operates from a single 1.8 V supply. The measured power consumption and the active chip area of the inverse sine function circuit are 350 μW and 0.15 mm2, respectively.
3 citations
01 Jul 1971
TL;DR: In this paper, the nth order derivatives of hyperbolic and trigonometric functions used in evaluating Fourier sine and cosine integrals are defined and studied. But they are not suitable for nth-order derivatives of trigonometrical functions.
Abstract: Formulas for nth order derivatives of hyperbolic and trigonometric functions used in evaluating Fourier sine and cosine integrals
3 citations