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Trygonometria: wartości i wzory redukcyjne

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RobertBendun 2022-02-27 21:51:16 +01:00
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trygonometria-liczby-zespolone.tex
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\documentclass[a5paper,10pt]{article} \documentclass[a5paper,8pt]{extarticle}
\usepackage{pl}
\usepackage[margin=1cm]{geometry}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[utf8]{inputenc}
\usepackage{polski}
\title{Trygonometria i liczby zespolone \\ \usepackage[margin=0.5cm]{geometry}
\large Algorytmy kwantowe} \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} \date{2021-02-27}
\author{Robert Bendun} \author{Robert Bendun}
\newcommand{\mi}{\mathrm{i}} \newcommand{\mi}{\mathrm{i}}
\renewcommand{\arraystretch}{1.5}
\begin{document} \begin{document}
\maketitle \maketitle
\section{Trygonometria} \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} \section{Liczby zespolone}
\subsection{Postać algebraiczna} \subsection{Postać algebraiczna}