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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10 citations
01 Jan 1998
TL;DR: The multipurpose algorithms used traditionally for real time digital signal processing (DSP), navigation and astronomy implementations are investigated and new directions for future implementations are presented.
Abstract: Trigonometric functions are used in many applications including real time digital signal processing (DSP), navigation and astronomy. Today’s demand for fast, small and portable equipment in those areas has resulted in the need for optimised structures for real-time processing of complex mathematical functions. Therefore, the multipurpose algorithms used traditionally for such implementations are investigated in this paper and new directions for future implementations are presented.
10 citations
TL;DR: In this paper, the frequency estimation of a nonstationary sinusoidal signal is studied and a new identification method is proposed to attenuate the noise influence, which does not require measuring or calculating derivatives of the input signal.
10 citations
TL;DR: In this paper, the authors proved two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873] using a method for proving inequalities of mixed trigonometric polynomial functions.
Abstract: In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.
10 citations
Book•
01 Jan 1990
TL;DR: In this paper, the authors present a model for solving problems in algebraically and graphically solvable problems with trigonometric functions, such as the Tangent Problem and the Area Problem.
Abstract: P. Prerequisites. Real Numbers. Cartesian Coordinate System. Linear Equations and Inequalities. Lines in the Plane. Solving Equations Graphically, Numerically and Algebraically. Solving Inequalities Algebraically and Graphically. 1. Functions and Graphs. Modeling and Equation Solving. Functions and Their Properties. Ten Basic Functions. Building Functions from Functions. Graphical Transformations. Modeling with Functions. 2. Polynomial, Power and Rational Functions. Linear and Quadratic Functions with Modeling. Power Functions with Modeling. Polynomial Functions of Higher Degree with Modeling. Real Zeros of Polynomial Functions. Complex Numbers. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions and Equations. Solving Inequalities in One Variable. 3. Exponential, Logistic and Logarithmic Functions. Exponential and Logistic Functions. Exponential and Logistic Modeling. Logarithmic Functions and Their Graphs. Properties of Logarithmic Functions. Equation Solving and Modeling. Mathematics of Finance. 4. Trigonometric Functions. Angles and Their Measures. Trigonometric Functions of Acute Angles. Trigonometry Extended: The Circular Functions. Graphs of Sine and Cosine: Sinusoids. Graphs of Tangent, Cotangent, Secant, and Cosecant. Graphs of Composite Trigonometric Functions. Inverse Trigonometric Functions. Solving Problems with Trigonometry. 5. Analytic Trigonometry. Fundamental Identities. Proving Trigonometric Identities. Sum and Difference Identities. Multiple-Angle Identities. Law of Sines. Law of Cosines. 6. Vectors, Parametric Equations, and Polar Equations. Vectors in the Plane. Dot Products of Vectors. Parametric Equations and Motion. Polar Coordinates. Graphs of Polar Equations. De Moivre's Theorem and nth Roots. 7. Systems and Matrices. Solving Systems of Two Equations. Matrix Algebra. Multivariate Linear Systems and Row Operations. Partial Fractions. Systems of Inequalities in Two Variables. 8. Analytic Geometry in Two and Three Dimensions. Conic Sections and Parabolas. Ellipses. Hyperbolas. Translations and Rotations of Axes. Polar Equations of Conics. Three Dimensional Cartesian Coordinate System. 9. Discrete Mathematics. Basic Combinatorics. The Binomial Theorem. Probability. Sequences and Series. Mathematical Induction. Statistics and Data (Graphical). Statistics and Data (Algebraic). 10. An Introduction to Calculus: Limits, Derivatives, and Integrals. Limits and Motion: The Tangent Problem. Limits and Motion: The Area Problem. More on Limits. Numerical Derivatives and Integrals.
10 citations