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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Book•
27 Oct 1995
TL;DR: In this paper, the authors present a list of the most important Quadratic Curves Linear Regression (QRL) functions and their Graphs, including Sine and Cosine Functions and Graphs of the Sine-Cosine Functions.
Abstract: 1 Numbers, Calculations and Basic Algebra The Integers and the Rational Numbers Real Numbers and their Properties Order and Averages Exponents and their Properties Polynomials and their Factors Rational Expressions The Complex Numbers 2 Equations and Inequalities Solving Equations Algebraically Equations and Applications Displaying Equations Geometrically Graphs with Graphics Calculators Inequalities and Absolute Values Lines Some Important Quadratic Curves Linear Regression 3 Functions and Their Graphs The Function Concept Linear Functions Quadratic Functions More on Graphics Calculators Polynomial Functions Rational Functions Combinations of Functions Inverse Functions Special Functions 4 Exponential and Logarithmic Functions Exponential Functions Logarithms and Logarithmic Functions Scientific Applications Business Applications Nonlinear Regression 5 The Trigonometric Functions Right Triangle Trigonometry General Angles and Arcs The Sine and Cosine Functions Graphs of the Sine and Cosine Functions Four More Trigonometric Functions Inverse Trigonometric Functions 6 Trigonometric Identities, Equations and Laws Basic Trigonometric Identities Addition Identities More Identities Trigonometric Equations The Law of Sines The Law of Cosines Vectors 7 Systems of Equations and Inequalities Equivalent Systems of Equations Solving Systems Using Matrices The Algebra of Matrices Inverses of Matrices Determinants Systems of Inequalities 8 Analytic Geometry Parabolas Ellipses Hyperbolas Rotations Parametric Equations Polar Coordinates Polar Equations of Conics 9 Sequences, Counting and Probability Arithmetic Sequences and Sums Geometric Sequences and Sums General Sequences and Programming Mathematical Induction The Binomial Formula Counting Ordered Arrangements Counting Unordered Collections Introduction to Probablility Independence in Probability Problems Answers to Selected Problems Index
3 citations
Patent•
05 Sep 2007TL;DR: In this paper, an analog-digital (A/D) converter was used to convert three-phase analog signals into 3-phase digital signals, and a digital signal processor (DSP) received the digital signals and executed computation with an inverse trigonometric function for a relatively linear range to obtain a rotation angle for a motor rotor.
Abstract: The device has an analog-digital (A/D) converter (22) converting three-phase analog signals into three-phase digital signals. A digital signal processor (DSP) (28) receives the digital signals and executes computation with an inverse trigonometric function for a relatively linear range to obtain a rotation angle for a motor rotor. A phase digitizer (24) changes the analog signals into digital phase signals, and a digital counter (26) converts the phase signals to produce a count value. The range is a realizable range between intersection points of the digital signals. An independent claim is also included for a method for calculating rotation angle of a motor rotor.
3 citations
08 May 1973
TL;DR: Algorithms for the automatic evaluation of elementary functions were studied to determine their suitability for hardware implementation, in terms of their accuracy, convergence rate, and hardware requirements.
Abstract: : Algorithms for the automatic evaluation of elementary functions were studied. Available algorithms obtained from current literature were analyzed to determine their suitability for hardware implementation, in terms of their accuracy, convergence rate, and hardware requirements. The functions considered were quotient, arctangent, cosine/sine, exponential, power function, logarithm, tangent, square root, and product. (Author)
3 citations
Posted Content•
TL;DR: In this paper, a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method was presented.
Abstract: This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function in the space dimension, with a weighted scheme. The scheme is shown to be unconditionally stable for a range of values using the von Neumann (Fourier) method. Several test problems are presented to confirm the accuracy of the new scheme and to show the performance of trigonometric basis functions. The proposed scheme is also computationally economical and can be used to solve complex problems. The numerical results are found to be in good agreement with known exact solutions and also with earlier studies.
3 citations
TL;DR: This paper describes the problem of selection of an appropriate branch of multiple-valued functions and discusses how to select FORTRAN functions "ATan" and "ATAN2', and how to evaluate the formula [arctan [EQUATION].
Abstract: This paper describes the problem of selection of an appropriate branch of multiple-valued functions. Real-valued arctangent function over real number filed is considered as an example. It is discussed how to select FORTRAN functions "ATAN" and "ATAN2', and how to evaluate the formula [arctan [EQUATION]. Minute post-conditioning is required for transferring the result of computer algebra to numerical computation.
3 citations