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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01 Jun 1981
TL;DR: In this article, the authors define the integral calculus as follows: 1. Integral Calculus: Definition of the integral Basic formulas of integral calculus The integration of rational functions, integration of certain non-rational functions Concept of definite integral Theorems on the definite integral, the integration of infinite series The improper integral The integral with infinite limits The gamma function Fourier series Index of definitions Subject index.
Abstract: Part One. Differential Calculus: Limits as $n=\infty$ Logarithms, powers, and roots Functions and continuity Limits as $x=\xi$ Definition of the derivative General theorems on the formation of the derivative Increase, decrease, maximum, minimum General properties of continuous functions on closed intervals Rolle's theorem and the theorem of the mean Derivatives of higher order Taylor's theorem "0/0" and similar matters Infinite series Uniform convergence Power series Exponential series and binomial series The trigonometric functions Functions of two variables and partial derivatives Inverse functions and implicit functions The inverse trigonometric functions Some necessary algebraic theorems Part Two. Integral Calculus: Definition of the integral Basic formulas of the integral calculus The integration of rational functions The integration of certain non-rational functions Concept of the definite integral Theorems on the definite integral The integration of infinite series The improper integral The integral with infinite limits The gamma function Fourier series Index of definitions Subject index.
25 citations
TL;DR: In this article, a control point form of quadratic trigonometric functions is developed which obeys all the properties of Bezier curve, and constraints are derived on these free parameters to interpolate positive, monotone and convex data.
Abstract: A control point form of quadratic trigonometric function is developed which obeys all the properties of Bezier curve. To preserve the shape of data, the quadratic trigonometric functions are transformed into $$GC^1$$
-interpolating functions. The $$GC^1$$
-interpolating functions have two free parameters in each subinterval to control the magnitude and direction of the tangent at the end points interval. Constraints are derived on these free parameters to interpolate positive, monotone and convex data. The order of approximation of developed interpolant is investigated as $$O( {h_{i}^{3}})$$
.
25 citations
01 Jan 2001
TL;DR: It is shown that interpolation and approximation by trigonometric polynomials provides a correct finite-dimensional discretization of the sampling problem for bandlimited functions.
Abstract: The chapter discusses the relation between finite-dimensional models of non-uniform sampling as they are used for numerical algorithms and the infinite-dimensional theory of non-uniform sampling of bandlimited functions. It is shown that interpolation and approximation by trigonometric polynomials provides a correct finite-dimensional discretization of the sampling problem for bandlimited functions. The results hold in arbitrary dimension and in particular they validate some recent fast reconstruction methods in dimension two.
24 citations
TL;DR: The Sumudu transform integral equation is solved by continuous integration by parts to obtain its definition for trigonometric functions, and the obtained result is inverted to show the expansion of trig onometric functions as an infinite series.
24 citations
TL;DR: In this paper, the authors introduce three different proofs of Priceos inequality and some new trigonometric and hyperbolic inequalities, and introduce a trigonometrical version of the Priceos inequalities.
Abstract: We introduce three different proofs of Priceos inequality and some new trigonometric and hyperbolic inequalities.
24 citations