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 2002
TL;DR: In this article, the authors present an approach for solving the problem of solving linear and logarithmic Equations in algebraically and numerically, and demonstrate the applicability of their approach to the real number system.
Abstract: 0. ALGEBRA REVIEW. The Real Number System. Special Topics: Decimal Representation of Real Numbers. Integral Exponents. Roots, Radicals, and Rational Exponents. Polynomials. Factoring. Rational Expressions. Chapter 0 Review. Discovery Project 0. 1. GRAPHS, LINES, AND TECHNOLOGY. The Coordinate Plane. Graphs and Graphing Technology. Lines. Linear Models. Chapter 1 Review. Discovery Project 1. 2. EQUATIONS AND INEQUALITIES. First-Degree Equations and Applications. Special Topics: Variation. Quadratic Equations and Applications. Solving Equations Graphically and Numerically. Polynomial, Radical, and Absolute Value Equations. Linear Inequalities. Polynomial and Rational Inequalities. Chapter 2 Review. Discovery Project 2. 3. FUNCTIONS AND GRAPHS. Functions. Functional Notation. Graphs of Functions. Special Topics: Parametric Graphing. Graphs and Transformations. Special Topics: Symmetry. Operations on Functions. Rates of Change. Special Topics: Instantaneous Rates of Change. Chapter 3 Review. Discovery Project 3. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions and Roots. Special Topics: Synthetic Division. Graphs of Polynomial Functions. Special Topics: Optimization Applications. Polynomial Models. Rational Functions. Special Topics: Other Rational Functions. Complex Numbers. The Fundamental Theorem of Algebra. Chapter 4 Review. Discovery Project 4. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Applications of Exponential Functions. Common and Natural Logarithmic Functions. Properties of Logarithms. Special Topics: Logarithms to Other Bases. Solving Exponential and Logarithmic Equations Algebraically. Exponential, Logarithmic, and Other Models. Inverse Functions. Chapter 5 Review. Discovery Project 5. 6. SYSTEMS OF EQUATIONS. Systems of Linear Equations in Two Variables. Special Topics: Systems of Nonlinear Equations. Large Systems of Linear Equations. Matrix Solution Methods. Matrix Methods for Square Systems. Special Topics: Matrix Algebra. Systems of Linear Inequalities. Introduction to Linear Programming. Chapter 6 Review. Discovery Project 6. 7. DISCRETE ALGEBRA. Sequences and Sums. Arithmetic Sequences. Geometric Sequences. Special Topics: Infinite Series. The Binomial Theorem. Permutations and Combinations. Special Topics: Distinguishable Permutations. Introduction to Probability. Mathematical Induction. Chapter 7 Review. Discovery Project 7. 8. ANALYTIC GEOMETRY. Circles and Ellipses. Hyperbolas. Parabolas. Special Topics: Rotations and Second-Degree Equations. Chapter 8 Review. Discovery Project 8. 9. TRIANGLE TRIGONOMETRY. Trigonometric Functions of Acute Angles. Trigonometric Functions of Angles. Applications of Right Triangle Trigonometry. The Law of Cosines. The Law of Sines. Special Topics: The Area of a Triangle. Chapter 9 Review. Discovery Project 9. 10. TRIGONOMETRIC FUNCTIONS. Angles and Radian Measure. Special Topics: Arc Length and Angular Speed. The Sine, Cosine, and Tangent Functions. Algebra and Identities. Basic Graphs. Periodic Graphs and Simple Harmonic Motion. Special Topics: Other Trigonometric Graphs. Other Trigonometric Functions. Chapter 10 Review. Discovery Project 10. 11. TRIGONOMETRIC IDENTITIES AND EQUATIONS. Basic Identities and Proofs. Addition and Subtraction Identities. Other Identities. Inverse Trigonometric Functions. Trigonometric Equations. Special Topics: Other Solution Methods for Trigonometric Equations. Chapter 11 Review. Discovery Project 11. 12. APPLICATIONS OF TRIGONOMETRY. Plane Curves and Parametric Equations. Polar Coordinates. The Complex Plane and Polar Form for Complex Numbers. DeMoivre's Theorem and nth Roots of Complex Numbers. Vectors in the Plane. Chapter 12 Review. Discovery Project 12. Geometry Review Appendix. Program Appendix.
1 citations
Book•
01 Jan 1988
TL;DR: Inequalities absolute value lines circles functions and their graphs limits continuity the derivative the chain rule trigonometric functions and derivatives Rolle's theorem, the mean value theorem and the sign of the derivative higher-order derivatives and implicit differentiation maxima and minima related rates curve sketching (graphs) applied maximum and minimum problems rectilinear motion approximation by differentials antiderivatives (indefinite integrals) the definite integral and the fundamental theorem of calculus area and arc length volume the natural logarithm exponential functions l"Hopital's rule exponential growth
Abstract: Inequalities absolute value lines circles functions and their graphs limits continuity the derivative the chain rule trigonometric functions and their derivatives Rolle's theorem, the mean value theorem and the sign of the derivative higher-order derivatives and implicit differentiation maxima and minima related rates curve sketching (graphs) applied maximum and minimum problems rectilinear motion approximation by differentials antiderivatives (indefinite integrals) the definite integral and the fundamental theorem of calculus area and arc length volume the natural logarithm exponential functions l"Hopital's rule exponential growth and decay inverse trigonometric functions integration by parts trigonometric integrands and substitutions integration by rational functions - the method of partial functions integrals for surface area, work, centroids improper integrals planar vectors parametric equations vector functions, curvilinear motion polar coordinates infinite sequences infinite series power series Taylor and MacLaurin series vectors in space, lines and planes functions of several variables partial derivatives directional derivatives and the gradient extreme values multiple integrals and their applications vector functions in space divergence and curl, line integrals differential equations.
1 citations
TL;DR: In the integration of numerous expressions, the results are expressible in the inverse trigonometric functions measured in radians as mentioned in this paper, and for three or four-place evaluations, the customary conversion-formulas may be applied to tables using the sexagesimal system.
Abstract: In the integration of numerous expressions, the results are expressible in the inverse trigonometric functions measured in radians. For three- or four-place evaluations, the customary conversion-formulas may be applied to tables using the sexagesimal system. For more than four places, the tables become bulky and inconvenient and the conversion tedious, especially when values are wanted to seven or more places. In 1927, the writer needed arctangents for torsion-balance calculations.
1 citations
TL;DR: The Cauchy residue theorem is one of the most important theorems in complex analysis at all times, and it is demonstrated that using the residue theorem to calculate some types of real improper integrals when the targeted integrals are hard or even impossible to deal with by conventional approaches as mentioned in this paper .
Abstract: The Cauchy’s residue theorem is one of the most important theorems in complex analysis at all times, and it is demonstrated that using the residue theorem is an easier and faster method to calculate some types of real improper integrals when the targeted integrals are hard or even impossible to deal with by conventional approaches. This paper considers several types of integrals including trigonometric integrals and integrals involving logarithmic function and power function. The general methods for calculating these integrals are presented and typical examples to illustrate how to use the methods are shown. The types of integrals in the paper are useful in many fields and have applications in the engineering and scientific research. In complex analysis, the residue theorem is a powerful tool for calculating the path integrals of analytic functions along closed curves, and can also be used to calculate the integrals of real functions.
1 citations