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•
01 Jan 2013
TL;DR: In this paper, the authors present a review of trigonometry and its application in linear coordinate systems, including the integration of volume under a curve and the area of a curve of revolution.
Abstract: Linear Coordinate Systems. Absolute Value. Inequalities * Rectangular Coordinate Systems * Lines * Circles * Equations and their Graphs * Functions * Limits * Continuity * The Derivative * Rules for Differentiating Functions * Implicit Differentiation * Tangent and Normal Lines * Law of the Mean. Increasing and Decreasing Functions * Maximum and Minimum Values * Curve Sketching. Concavity. Symmetry * Review of Trigonometry * Differentiation of Trigonometric Functions * Inverse Trigonometric Functions * Rectilinear and Circular Motion * Related Rates * Differentials. Newton's Method * Antiderivatives * The Definite Integral. Area under a Curve * The Fundamental Theorem of Calculus * The Natural Logarithm * Exponential and Logarithmic Functions * L'Hopital's Rule * Exponential Growth and Decay * Applications of Integration I: Area and Arc Length * Applications of Integration II: Volume * Techniques of Integration I: Integration by Parts * Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions * Techniques of Integration III: Integration by Partial Fractions * Miscellaneous Substitutions * Improper Integrals * Applications of Integration II: Area of a Surface of Revolution * Parametric Representation of Curves * Curvature * Plane Vectors * Curvilinear Motion * Polar Coordinates * Infinite Sequences * Infinite Series * Series with Positive Terms. The Integral Test. Comparison Tests * Alternating Series. Absolute and Conditional Convergence. The Ratio Test * Power Series * Taylor and Maclaurin Series. Taylor's Formula with Remainder * Partial Derivatives * Total Differential. Differentiability. Chain Rules * Space Vectors * Surface and Curves in Space * Directional Derivatives. Maximum and Minimum Values * Vector Differentiation and Integration * Double and Iterated Integrals * Centroids and Moments of Inertia of Plane Areas * Double Integration Applied to Volume under a Surface and the Area of a Curved Surface * Triple Integrals * Masses of Variable Density * Differential Equations of First and Second Order
3 citations
3 citations
01 Jan 1985
TL;DR: In this paper, Ramanujan gives more proofs in this chapter than in most of the later chapters, and several of the formulas are very intriguing and evince the ingenuity and cleverness of the author.
Abstract: Chapter 2 is fairly elementary, but several of the formulas are very intriguing and evince Ramanujan’s ingenuity and cleverness. Ramanujan gives more proofs in this chapter than in most of the later chapters.
3 citations
3 citations
Patent•
06 Nov 2007TL;DR: In this paper, a two-dimensional inverse discrete cosine transform function is implemented, where each of the two functions is controlled to operate on a matrix of coefficients in either of two different directions.
Abstract: Implementing a two-dimensional inverse discrete cosine transform function includes executing two one-dimensional inverse discrete cosine transforming functions. Each of the one-dimensional functions is controlled to operate on a matrix of coefficients in either of two different directions.
3 citations