diff --git a/jan-may-2022-latex/NA21B005/NA21B005.tex b/jan-may-2022-latex/NA21B005/NA21B005.tex index e0400fd..2f6b236 100644 --- a/jan-may-2022-latex/NA21B005/NA21B005.tex +++ b/jan-may-2022-latex/NA21B005/NA21B005.tex @@ -1,2 +1,38 @@ -\section{NA21B005} -Student shall edit this file and include stuff for the assignment +\documentclass{article} +\usepackage[margin=1in]{geometry} + + +\title{Euler’s Identity} +\author{Amar Nath Singh NA21B005} +\date{June 2022} + +\begin{document} + +\maketitle + +\section{Euler’s Identity} +\begin{equation} + e^{i\pi} + 1 = 0 +\end{equation} +\\ +A very famous equation, Euler’s identity relates the seemingly random values of pi, e, and the square root of -1. It is considered by many to be the most beautiful equation in mathematics. + +A more general formula is + +\begin{equation} + e^{i x} = \cos x + i \sin x +\end{equation} +\\ +When x = $\pi$ , the value of $\cos$ x & is -1, while i$\sin x$ is 0, resulting in Euler’s identity, as -1 + 1 = 0.\\ \\ +\begin{center} +\begin{tabular}{ |l|l| } + \hline + $\pi$ & The number $\pi$ is a mathematical constant that is approximately equal to 3.14159. \\ + $e$ & It is the base of the natural logarithms, approximately equal to 2.71828.\\ + $i$ & The value of i is $\sqrt{-1}$.\\ + $\cos$ & cosine are trigonometric functions of an angle.\\ + $\sin$ & sine are trigonometric functions of an angle.\\ + \hline +\end{tabular} +\end{center} +\end{document}