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% !TeX encoding = UTF-8
% !TeX spellcheck = sl_SI
% do-vimlatex-onwrite
\documentclass[]{article}
\usepackage[utf8]{inputenc}
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\usepackage[hidelinks]{hyperref}
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\usepackage{graphicx}
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\usepackage[inline]{enumitem}
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\usepackage{amsmath}
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\usepackage{filecontents}
\usepackage{textcomp}
\usepackage{tkz-euclide}
\usepackage{dirtytalk}
\usepackage{csquotes}
\usepackage{listings}
\usepackage{datetime} % [ddMMyyyy]
\usepackage{ccicons}
\usepackage{chemformula}
\usepackage{gensymb}
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\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
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\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}
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\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 $$\frac{\sin\ang{210}-\cos\ang{270}}{\tan\ang{135}\cdot\cot\ang{315}-\sin\ang{300}}
=\frac{-\sin\ang{30}-0}{\frac{\sin{135}}{\cos{135}}\cdot\frac{\cos\ang{315}}{\sin\ang{315}}+\sin\ang{60}}=$$
$$=\frac{-\sin\ang{60}}{1+\sin\ang{60}}=-\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}
=-\frac{1}{2\left(\frac{\sqrt{3}}{2}+1\right)}=-\frac{1}{2\cdot\frac{\sqrt{3}+2}{2}}=-\frac{1}{2\left(\sqrt{3}+2\right)}
=-\frac{1}{\sqrt{3}+2}=-\frac{2-\sqrt{3}}{\left(\sqrt{3}+2\right)\left(\sqrt{2-\sqrt{3}}\right)}=$$
$$=\sqrt{3}-2$$
\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}
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