Showing papers on "Inverse trigonometric functions published in 2002"

A new algorithm for point-in-polygon test

Abstract: An original point-in-polygon test, based upon an electric analogy, is illustrated. It enhances an analogous procedure, previously developed by the first author [5], by almost halving the computer time required to numerically perform the test. The result is obtained by proving an addition formula for the inverse tangent function that corrects the one which can be usually found in mathematical handbooks. Further, the equivalence of the proposed method with the sum of angles method is shown.

On some trigonometric power sums

Abstract: Using the generating function method, the closed formulas for various power sums of trigonometric functions are established. The computer algebra system Maple is used to carry out the complex calculations.

Real-Life Math: Everyday Use of Mathematical Concepts

Abstract: Introduction Angle Asymptote Cartesian Coordinates Circles Circumference Complex Numbers Conic Sections Counting Derivative Equations Expected Value Exponential Decay Exponential Growth Fibonacci Sequence Imaginary Numbers Integration Inverse (Multiplicative) Inverse Function Inverse Square Function Linear Functions Logarithms Logistic Functions Matrices Perimeter Periodic Functions Plane Polar Coordinates Polynomial Functions Probability Proportions Pythagorean Theorem Quadratic Functions Quadrilaterals Rate Ratio Reflections Rotations Sequence Series Similarity Slope Square Roots Standard Deviation Step Functions Surface Area Symbolic Logic Symmetry Tangent Translations Triangle Trigonometry Variation Vectors Volume References Index

Method of obtaining correctly rounded results in ieee double precision format of transcendental functions

Abstract: A method for correctly rounding a result of transcendental function such as sine, cosine, tangent, arc tangent, exponent, logarithm, or power in double precision arithmetic is disclosed. All arguments of the functions that are undefined, overflow or underflow are fist purged off. Then the given argument is reduced within a primary range to compute the function as a pair of double precision numbers. Multi-precision arithmetic with a specified word length is used if the sum of the pair of double precision number is close to the boundary case. The multi-precision arithmetic is repeated with greater precision each time until the result of the multi-precision arithmetic is not close to the boundary case. The result of the multi-precision arithmetic or the sum of said pair of double precision numbers is finally rounded according to the given rounding mode.

Contemporary college algebra and trigonometry: A graphing approach

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.

Time measurement circuit

Abstract: PROBLEM TO BE SOLVED: To measure time over a wide dynamic range, with high stability and a high accuracy. SOLUTION: A standard clock synchronous to a trigonometric function wave of a sine wave and a cosine wave is generated at a standard pulse generation circuit 12. Two kinds of the trigonometric function waves are A/D converted by ADC 16, 18 with a timing of arrival of a start signal, and this value is subjected to inverse trigonometric function operation by an operation processing device 46 to calculate a micro time at a start side. A sine time at a stop side is also calculated similarly. A pulse is generated at an AND circuit 40 between synchronous start and stop signals taking a synchronism at FF 24, 38 and is counted by a scaler 42 and a count number at the time of stop is stored in a register. The operation processing device 46 calculates the overall measurement time using the count number, clock period time and two micro times.

Extracting the phase of an OFDM signal sample

Abstract: The disclosed embodiments relate to exploiting circuitry that exists in a typical Orthogonal Frequency Division Multiplexing (OFDM) receiver to find the phase of a complex number corresponding to an input signal without implementing additional costly circuitry or employing a relatively slow inverse tangent look-up table. The magnitude of the complex number is normalized and processed through a closed loop to produce an output proportional to the phase of the complex number.