36 - Trigonometric functions and general formulae

Abstract

This chapter provides trigonometric functions and general formulae for mathematical operations, and discusses the commonly used mathematical signs and symbols. The chapter further illustrates the applications of trigonometric formulae in approximations for small angles, for calculating the solution of triangles, and also for the spherical triangle. Also discussed here are the exponential form, De Moivre's theorem, Euler's relation, and the hyperbolic functions. The inclusion of the complex variable in trigonometric equations using the Argand diagram has been elaborated in the chapter. This is followed by the Cauchy-Riemann equations and Cauchy's theorem, which calculates the value of a function at a point in the interior of a closed curve in terms of the values on that curve. The application of zeroes, poles, and residues are then detailed using the Taylor series. Regarding coordinate systems, the cylindrical coordinates and spherical polar coordinates are formulated. The chapter further discusses the transformation of integrals and Laplace's equation. In the section on solution of equations, calculations are given for the quadratic equation, the bisection method, the Regula Falsi, the fixed-point iteration, and Newton's method. In conclusion, the method of least squares is also discussed, and the relationship among decibels, current, voltage ratio, and power ratio is provided.