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+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+% do-vimlatex-onwrite
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\usepackage{xurl} % da breaka url
+\usepackage[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{siunitx}
+\usepackage{multicol}
+\usepackage{tabularcalc}
+\usepackage{amsmath}
+\usepackage{float}
+\usepackage{tasks}
+\usepackage{filecontents}
+\usepackage{textcomp}
+\usepackage{tkz-euclide}
+\usepackage{dirtytalk}
+\usepackage{csquotes}
+\usepackage{listings}
+\usepackage{datetime} % [ddMMyyyy]
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+\usepackage{tabularx}
+\usepackage{xcolor}
+\usepackage{colortbl}
+\usepackage{exsheets}
+\usepackage{harpoon}
+\usepackage{readarray}
+\usepackage{forloop}
+\usepackage[nomessages]{fp}
+\usepackage{multirow}
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codered}{rgb}{1,0,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\renewcommand{\dateseparator}{. }
+\settimeformat{hhmmsstime}
+\lstdefinestyle{mystyle}{
+	backgroundcolor=\color{backcolour},   
+	commentstyle=\color{codegreen},
+	keywordstyle=\color{magenta},
+	numberstyle=\tiny\color{codegray},
+	stringstyle=\color{codepurple},
+	basicstyle=\ttfamily\footnotesize,
+	breakatwhitespace=false,         
+	breaklines=true,                 
+	captionpos=b,                    
+	keepspaces=true,                 
+	numbers=left,                    
+	numbersep=5pt,                  
+	showspaces=false,                
+	showstringspaces=false,
+	showtabs=false,                  
+	tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
+	\newpage
+	\null
+	\vskip 2em%
+	\begin{center}%
+		\let \footnote \thanks
+		{\LARGE \@title \par}%
+		\vskip 1.5em%
+		{\large
+			\lineskip .5em%
+			\begin{tabular}[t]{c}% <------
+				\@author%            <------ Authors
+			\end{tabular}\par}%    <------
+		\vskip 1em%
+		{\large \@date}%
+	\end{center}%
+	\par
+	\vskip 1.5em}
+%opening
+\newcommand{\snovdn}{Kotne funkcije poljubnih kotov }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{25}
+\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
+\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
+\makeatletter
+\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
+\newcommand{\@xslalph}[1]{%
+	\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
+	\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
+	\or t\or u\or v\or z\or \v{z}
+	\else\@ctrerr\fi%
+}
+\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+	\frac{\text{#1}}{\text{#2}}
+}
+\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
+\newcommand\vektor{\overrightarrow}
+\newcommand{\iic}{I\textsuperscript{2}C }
+\title{%
+	\snovdn --- \stevilkadn. domača naloga
+	\\
+	\large Matematika, Gimnazija Bežigrad}
+\author{\begin{tabular}{rl}
+		\textbf{Profesor:} & prof. Vilko Domajnko \\
+		\textbf{Avtor:} & Anton Luka Šijanec, 2. a
+%		\textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
+\end{tabular}}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}%
+\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} 
+% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+\begin{abstract}
+Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam. Kjer je bilo potrebno izbirati neke poljubne naloge, sem jih vselej izbral naključno.
+\end{abstract}
+\paragraph{Navodilo naloge} \textbf{vaje2:} 80 / 551, 552, 553, 554 (povsod po en primer)
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\setcounter{enumi}{550}
+	\item Izračunaj natančne vrednosti vseh štirih kotnih funkcij za dane kote.
+		\begin{enumerate}[label=\textbf{\xslalph*)}]
+			\item $\ang{120}$
+				$$\sin\ang{120}=\sin\ang{60}=\frac{\frac{a\sqrt{3}}{2}}{a}=\frac{\sqrt{3}}{2}$$
+		\end{enumerate}
+	\item Natančno izračunaj.
+		\begin{enumerate}[label=\textbf{\xslalph*)}]
+			\setcounter{enumii}{4}
+			\item $$\frac{\sin\ang{210}-\cos\ang{270}}{\tan\ang{135}\cdot\cot\ang{315}-\sin\ang{300}}
+				=\frac{-\sin\ang{30}-0}{\frac{\sin{135}}{\cos{135}}\cdot\frac{\cos\ang{315}}{\sin\ang{315}}+\sin\ang{60}}=$$
+				$$=\frac{-\sin\ang{60}}{1+\sin\ang{60}}=-\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}
+				=-\frac{1}{2\left(\frac{\sqrt{3}}{2}+1\right)}=\frac{1}{2\cdot\frac{\sqrt{3}+2}{2}}=-\frac{1}{2\left(\sqrt{3}+2\right)}
+				=\frac{1}{\sqrt{3}+2}=\frac{2-\sqrt{3}}{\left(\sqrt{3}+2\right)\left(\sqrt{2-\sqrt{3}}\right)}=$$
+				$$=2-\sqrt{3}$$
+		\end{enumerate}
+	\item Naj bo $\alpha$ kot, za katerega velja $\ang{0}\leq\alpha\leq\ang{360}$. V enotskem krogu načrtaj in nato še zapiši v stopinjah vse velikosti kotov $\alpha$, za katere velja:
+		\begin{enumerate}[label=\textbf{\xslalph*)}]
+			\setcounter{enumii}{6}
+			\item $\cot\alpha=-1$
+				\begin{multicols}{2}
+					\begin{center}
+						\begin{tikzpicture}[scale=2.5]
+							\tkzDefPoint(0,0){O} \tkzDefPoint(1,0){V} \tkzDefPoint(-1,0){Z} \tkzDefPoint(0,1){S} \tkzDefPoint(0,-1){J}
+							\tkzDefPoint(1,-1){A} \tkzDefPoint(-1,1){B}
+							\tkzDrawCircle(O,S) \tkzDrawLine(S,J) \tkzDrawLine(V,Z), \tkzDrawLine(O,A) \tkzDrawLine(O,B)
+							\tkzDrawPoints(O,S,J,V,Z,A,B) \tkzLabelPoints(O,S,J,V,Z,A,B)
+							\tkzMarkAngle[size=.25](V,O,A)
+							\tkzFillAngle[fill=red!30, opacity=.3, size=.25](V,O,A)
+							\tkzLabelAngle[pos=.125](V,O,A){$\alpha$}
+							\tkzMarkAngle[size=.5](V,O,B)
+							\tkzFillAngle[fill=blue!30, opacity=.3, size=.5](V,O,B)
+							\tkzLabelAngle[pos=.25](V,O,B){$\alpha$}
+						\end{tikzpicture}
+					\end{center}
+					$$\alpha=\{\ang{315}, \ang{135}\}$$
+				\end{multicols}
+		\end{enumerate}
+	\item Izračunaj velikost kota $\chi$, če je kot:
+		\begin{enumerate}[label=\textbf{\xslalph*)}]
+			\setcounter{enumii}{6}
+			\item velik med \ang{180} in \ang{360} in zanj velja $\cos\chi=0,2$. Zaokroži na minuto natančno.
+				$$\sin\left(\alpha+\ang{270}\right)=0,2\rightarrow\arcsin0,2=\alpha+\ang{270}\Dot=\ang{11,536959}+\ang{270}
+				=\ang{281,536959}\Dot=\ang{281}32'$$
+				
+		\end{enumerate}
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.}
+izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
+\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi 
+\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je  \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
+\if\razhroscevanje1
+\vfill
+\section*{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
+
+Grafi imajo natančnost \functionSamples\space točk na graf.
+
+Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+%	\item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}