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.

Linear amplification using nonlinear devices and inverse sine phase modulation

Abstract: A linear amplification providing a replica of an input signal having amplitude variations is accomplished at frequencies and power levels for which linear gain elements are not available. Linear amplification is provided by separating an original bandpass input signal into two components, one of which is a constant amplitude sinusoidal component and the other of which is a low-pass envelope signal. The envelope signal is processed to produce both an inverse sine, phase modulated signal and the complex conjugate of the modulated signal. The phase variations of the modulated signal and of its complex conjugate are proportional to the inverse sine of the envelope. The modulated signal and its complex conjugate are each separately mixed with the constant amplitude sinusoidal signal to produce two constant amplitude signals which are filtered and amplified by either linear or nonlinear devices. The amplified filtered resultants are combined to produce a linearly amplified replica of the original bandpass input signal.

q-Extension of the Euler formula and trigonometric functions

Abstract: In this paper, we introduce a Daehee constant, the so-called q-extension of the Napier constant, and consider the Daehee formula associated with the q-extensions of trigonometric functions. That is, we derive the q-extensions of sine and cosine functions from our Daehee formula. Finally, we present the q-calculus related to the q-extensions of sine and cosine functions.

CRC Standard Curves and Surfaces with Mathematica

Abstract: Introduction Concept of a Curve Concept of a Surface Coordinate Systems Qualitative Properties of Curves and Surfaces Classification of Curves and Surfaces Basic Curve and Surface Operations Method of Presentation References Algebraic Functions Plotting Information for This Chapter Functions with xn/m Functions with xn and (a + bx)m Functions with (a2 + x 2) and xm Functions with (a2 x2) and xm Functions with (a3 + x3) and xm Functions with (a3 x3) and xm Functions with (a4 + x4) and xm Functions with (a4 x4) and xm Functions with a + bx and xm Functions with a2 x2 and xm Functions with x2 a2 and xm Functions with a2 + x2 and xm Miscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressed Parametrically Transcendental Functions Plotting Information for This Chapter Functions with sinn (2 ax) and cosm(2 bx)(n,m integers) Functions with 1 +/- sinn (2 ax) and 1 +/-} cosm (2 bx) Functions with c sinn (ax) + d cosm (bx) Functions of More Complicated Arguments Inverse Trigonometric Functions Logarithmic Functions Exponential Functions Hyperbolic Functions Inverse Hyperbolic Functions Trigonometric Combined with Exponential Functions Trigonometric Functions Combined with Powers of x Logarithmic Functions Combined with Powers of x Exponential Functions Combined with Powers of x Hyperbolic Functions Combined with Powers of x Combined Trigonometric Functions, Exponential Functions, and Powers of x Miscellaneous Functions Functions Expressible in Polar Coordinates Functions Expressible Parametrically Polynomial Sets Plotting Information for This Chapter Orthogonal Polynomials Nonorthogonal Polynomials References Special Functions in Mathematical Physics Plotting Information for This Chapter Exponential and Related Integrals Sine and Cosine Integrals Gamma and Related Functions Error Functions Fresnel Integrals Legendre Functions Bessel Functions Modified Bessel Functions Kelvin Functions Spherical Bessel Functions Modified Spherical Bessel Functions Airy Functions Riemann Functions Parabolic Cylinder Functions Elliptic Integrals Jacobi Elliptic Functions References Green's Functions and Harmonic Functions Plotting Information for This Chapter Green's Function for the Poisson Equation Green's Function for the Wave Equation Green's Function for the Diffusion Equation Green's Function for the Helmholtz Equation Miscellaneous Green's Functions Harmonic Functions: Solutions to Laplace's Equation References Special Functions in Probability and Statistics Plotting Information for This Chapter Discrete Probability Densities Continuous Probability Densities Sampling Distributions Laplace Transforms Plotting Information for This Chapter Elementary Functions Algebraic Functions Exponential Functions Trigonometric Functions References Nondifferentiable and Discontinuous Functions Plotting Information for This Chapter Functions with a Finite Number of Discontinuities Functions with an Infinite Number of Discontinuities Functions with a Finite Number of Discontinuities in First Derivative Functions with an Infinite Number of Discontinuities in First Derivative Random Processes Plotting Information for This Chapter Elementary Random Processes General Linear Processes Integrated Processes Fractal Processes Poisson Processes References Polygons Plotting Information for This Chapter Polygons with Equal Sides Irregular Triangles Irregular Quadrilaterals Polyiamonds Polyominoes Polyhexes Miscellaneous Polygons Three-Dimensional Curves Plotting Information for This Chapter Helical Curves Sine Waves in Three Dimensions Miscellaneous 3-D Curves Knots Links References Algebraic Surfaces Plotting Information for This Chapter Functions with ax + by Functions with x2/a2 +/- y2/b2 Functions with x2/a2 + y2/b2 +/-c2)1/2 Functions with x3/a3 +/- y3/b3 Functions with x4/a4 +/- y4/b4 Miscellaneous Functions Miscellaneous Functions Expressed Parametrically Transcendental Surfaces Plotting Information for This Chapter Trigonometric Functions Logarithmic Functions Exponential Functions Trigonometric and Exponential Functions Combined Surface Spherical Harmonics Complex Variable Surfaces Plotting Information for This Chapter Algebraic Functions Transcendental Functions Minimal Surfaces Plotting Information for This Chapter Elementary Minimal Surfaces Complex Minimal Surfaces References Regular and Semi-Regular Solids with Edges Plotting Information for This Chapter Platonic Solids Archimedean Solids Duals of Platonic Solids Stellated (Star) Polyhedra References Irregular and Miscellaneous Solids Plotting Information for This Chapter Irregular Polyhedra Miscellaneous Closed Surfaces with Edges Index

A direct relation between a signal time series and its unwrapped phase

Abstract: A noniterative method for phase unwrapping a real, finite-length, discrete-time signal is described. We use an operator which counts sign changes in a Sturm sequence generated from the real and imaginary parts of the DFT. The number of sign changes is related to the number of multiples of π which must be added to the principal value arctan to produce unwrapped phase. Except for the evaluation of trigonometric and inverse trigonometric functions, the unwrapped phase at any frequency can be computed in a finite number of steps. The approach is illustrated with an example, and a Fortran program implementation of the algorithm is included in the Appendix.