diff --git a/trygonometria-liczby-zespolone.tex b/trygonometria-liczby-zespolone.tex index 01cd5e9..1ce074b 100644 --- a/trygonometria-liczby-zespolone.tex +++ b/trygonometria-liczby-zespolone.tex @@ -1,24 +1,69 @@ -\documentclass[a5paper,10pt]{article} -\usepackage{pl} -\usepackage[margin=1cm]{geometry} -\usepackage{amsmath} -\usepackage{amsfonts} -\usepackage[utf8]{inputenc} -\usepackage{polski} +\documentclass[a5paper,8pt]{extarticle} -\title{Trygonometria i liczby zespolone \\ - \large Algorytmy kwantowe} +\usepackage[margin=0.5cm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{gensymb} +\usepackage{polski} +\usepackage{multirow} + +\title{Trygonometria i liczby zespolone \\ \large Algorytmy kwantowe} \date{2021-02-27} \author{Robert Bendun} \newcommand{\mi}{\mathrm{i}} +\renewcommand{\arraystretch}{1.5} + \begin{document} \maketitle \section{Trygonometria} +\subsection{Wartości} + +\begin{center} +\begin{tabular}{ |c|c|c|c|c|c| } \hline + $\alpha$ (deg) & $0\degree$ & $30\degree$ & $45\degree$ & $60\degree$ & $90\degree$ \\ \hline + $\alpha$ (rad) & $0$ & $\frac{\pi}{6}$ & $\frac{\pi}{4}$ & $\frac{\pi}{3}$ & $\frac{\pi}{2}$ \\ \hline + $\sin$ & $0$ & $\frac{1}{2}$ & $\frac{\sqrt{2}}{2}$ & $\frac{\sqrt{3}}{2}$ & $1$ \\ \hline + $\cos$ & $1$ & $\frac{\sqrt{3}}{2}$ & $\frac{\sqrt{2}}{2}$ & $\frac{1}{2}$ & $0$ \\ \hline +\end{tabular} +\end{center} + +\subsection{Wzory redukcyjne} + +\begin{center} +\begin{tabular}{ c | c | c | c } + \multicolumn{2}{c|}{$ \sin -\alpha = -\sin \alpha $} & + \multicolumn{2}{c}{$ \cos -\alpha = \sin \alpha $} \\ \hline + + $ \sin \left( \frac{\pi}{2} - \alpha \right) = \cos \alpha $ & + $ \sin \left( \frac{\pi}{2} + \alpha \right) = \cos \alpha $ & + $ \cos \left( \frac{\pi}{2} - \alpha \right) = \sin \alpha $ & + $ \cos \left( \frac{\pi}{2} + \alpha \right) = -\sin \alpha $ \\ + + $ \sin \left( \pi - \alpha \right) = \sin \alpha $ & + $ \sin \left( \pi + \alpha \right) = -\sin \alpha $ & + $ \cos \left( \pi - \alpha \right) = -\cos \alpha $ & + $ \cos \left( \pi + \alpha \right) = -\cos \alpha $ \\ + + \hline + + $ \sin \left( \frac{3\pi}{2} - \alpha \right) = -\cos \alpha $ & + $ \sin \left( \frac{3\pi}{2} + \alpha \right) = -\cos \alpha $ & + $ \cos \left( \frac{3\pi}{2} - \alpha \right) = -\sin \alpha $ & + $ \cos \left( \frac{3\pi}{2} + \alpha \right) = \sin \alpha $ \\ + + $ \sin \left( 2\pi - \alpha \right) = -\sin \alpha $ & + $ \sin \left( 2\pi + \alpha \right) = \sin \alpha $ & + $ \cos \left( 2\pi - \alpha \right) = \cos \alpha $ & + $ \cos \left( 2\pi + \alpha \right) = \cos \alpha $ +\end{tabular} +\end{center} + \section{Liczby zespolone} \subsection{Postać algebraiczna}