Showing papers on "Inverse trigonometric functions published in 1984"
Book•
01 Jan 1984
TL;DR: In this paper, the authors introduce the notion of derivatives of algebraic functions, including trigonometric, logarithmic, and exponential functions, and apply them to algebraic problems.
Abstract: Numerical Computation. Introduction to Algebra. Simple Equations and Word Problems. Functions. Graphs. Geometry. Right Triangles and Vectors. Factors and Factoring. Fractions and Fractional Equations. Systems of Linear Equations. Determinants. Matrices. Exponents and Radicals. Quadratic Equations. Oblique Triangles and Vectors. Radian Measure, Arc Length, and Rotation. Graphs of the Trigonometric Functions. Trigonometric Identities and Equations. Ratio, Proportion, and Variation. Exponential and Logarithmic Functions. Complex Numbers. Analytic Geometry. Binary, Hexadecimal, Octal, and BCD Numbers. Inequalities and Linear Programming. Sequences, Series, and the Binomial Theorem. Introduction to Statistics and Probability. Derivatives of Algebraic Functions. Graphical Applications of the Derivative. More Applications of the Derivative. Integration. Applications of the Integral. More Applications of the Integral. Derivatives of Trigonometric, Logarithmic, and Exponential Functions. Methods of Integration. Differential Equations. Solving Differential Equations by the Laplace Transform and by Numerical Methods. Infinite Series. Appendices. Indexes.
7 citations
Book•
01 Jan 1984
TL;DR: In this article, the authors define the concept of a function as a graph of a real number and apply it to the problem of finding a function that maximizes the average rate of change of the real number.
Abstract: 1. FUNDAMENTALS. Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles. 2. EQUATIONS AND INEQUALITIES. Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Applications to Optimization. Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. TRIGONOMETRIC FUNCTIONS OF ANGLES. Trigonometric Functions of Acute Angles. Algebra and the Trigonometric Functions. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities. 7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS. Radian Measure. Radian Measure and Geometry. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 8. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 9. ADDITIONAL TOPICS IN TRIGONOMETRY. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates. 10. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities. 11. ANALYTIC GEOMETRY. The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes. 12. ROOTS OF POLYNOMIAL EQUATIONS. The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions. 13. ADDITIONAL TOPICS. Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem. Appendix 1: Using a Graphing Utility. Appendix 2: Significant Digits and Calculators. Tables. Answers to Selected Exercises. Index.
6 citations
TL;DR: In this article, the integrals of the form r/2 e-o'cos" OdO, r/ 2 e-pesmede Jo Jo (p real, Re(^) > -1) are expressed in terms of Gamma and hypergeometric functions for integer and noninteger values of q snap.
Abstract: Integrals of the form r/2 e-o'cos\" OdO, r/2e'Pesm\"ede Jo Jo (p real, Re(^) > -1) are expressed in terms of Gamma and hypergeometric functions for integer and noninteger values of q snap. The results include those of [2] as special cases. Introduction. The integrals considered here are /•ir/2 '0 fir/2 (1) ( e'^cos\" OdO, Jo (2) r/2 eipesin\" 0d6, Jo where p is real, and Re(^r) > -1. Values for some of the above integrals are recorded in [1, art. 3.631], but only for special (or integer) values of \"q \", and not always in closed form. The integrals (1) and (2) are, of course, related since, with the change of variable 0 -» 7r/2 6,(2) becomes (3) i\"72 e\"\"W0dO = eiín,/2 fv/2 e^cos«0 dO Jo Jo resulting in the following relations:
2 citations