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.
Papers published on a yearly basis
Papers
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01 Jan 2014
TL;DR: In this article, an FPGA implementation of window filtering using Coordinate Rotation Digital Computer (CORDIC) algorithm by replacing linear CORDIC with multiple shift-add network and conventional circular CordIC processor is presented.
Abstract: Window filtering is a well-known processing technique for limiting any signal to short time segment in various fields, like audio or video signal processing, communication systems etc. The Coordinate Rotation Digital Computer (CORDIC) is an arithmetic technique, which makes it possible to perform two dimensional rotations using simple hardware components. The algorithm can be used to evaluate elementary functions such as cosine, sine, arctangent, sinh, cosh, tanh, ln and exp. Here FPGA implementation of various window- functions using CORDIC algorithm by replacing linear CORDIC with multiple shift-add network and conventional circular CORDIC processor by a completely scaling-free
TL;DR: In this article, the authors present an approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. But this approach is not suitable for algebraic integration.
Abstract: Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals. It introduces a framework in which students can better understand more advanced mathematical ideas such as the inverse Laplace transform and also affords an opportunity to work with detailed algebraic manipulations involving the binomial expansion.
Patent•
27 Jul 2001
TL;DR: In this paper, a phase detector circuit is used for a direct evaluation of phase error without filter, and comprises a tracker-holder, which can be used for division, multiplication, and summation.
Abstract: The electronic circuit for the generation of an output analogue signal corresponding to at least one mathematical operation on the basis of at least two input analogue signals, comprises a set of sub-circuits which can deliver a signal corresponding to the square-root of product of input signals, that is of the form 2 square root (I1I2), and a circuit for delivering a signal corresponding to the raising to the power of 2 of input signal, that is of the form K.Vin . The electronic circuit comprises a generator with an input receiving an analogue signal x(t), and an output delivering a signal f(x), which is given analytically. The electronic circuit comprises a differential pair, and also means for division, multiplication and summation. A phase detector circuit comprises a generator of analogue signal of inverse trigonometric type. A frequency synthesizer with a phase-locked loop (PLL), utilized in radio-telephones, comprises a circuit for the generation of a signal as a function of phase-shift, which incorporates specified circuits. The method for the generation of analogue signal as a function of phase-shift between two analogue signals is by use of specified circuit to obtain the analogue signal f(x) given analytically and corresponding to inverse sine and cosine, and also another analytical form corresponding to inverse tangent and cotangent. The maximum error with respect to exact values of inverse sine is 0.22%. An application of electronic circuit is for measuring the phase-shift of impedance and the in-circuit test of application of electronic circuit is for measuring the phase-shift of impedance and the in-circuit test of PCB. The equipment for the generation of output signal corresponding to the application of one of specified mathematical operations comprises an electronic circuit of proposed type. The phase detector specified mathematical operations comprises an electronic circuit of proposed type. The phase detector circuit is used for a direct evaluation of phase error without filter, and comprises a tracker-holder.
Journal Article•
TL;DR: This article used APOS theory to study students' construction of the sine and cosine functions and their inverses, and found that the constructions students would need to do in order to attain a process conception of these functions are tested by using semi-structured interviews with a group of 11 students.
Abstract: This study uses APOS Theory to study students’ construction of the sine and cosine functions and their inverses. The conjecture of the constructions students would need to do in order to attain a process conception of these functions is tested by using semi-structured interviews with a group of 11 undergraduate students. Analysis of the interviews suggests a small number of basic mental constructions that students would need to do, that account for observed difficulties, and that hence would need to be stressed during instruction.