summaryrefslogblamecommitdiffstats
path: root/mat/domace_naloge/11/dokument.tex
blob: 6bf78f47b609d63444c01182f1b0bad4dbaba3ae (plain) (tree)














































































































































































































































































                                                                                                                                                                                                                                                                                                                                                                                                                               
% !TeX encoding = UTF-8
% !TeX spellcheck = sl_SI
% do-vimlatex-onwrite
\documentclass[]{article}
\usepackage[utf8]{inputenc}
\usepackage{etoolbox}
\usepackage[hidelinks]{hyperref}
\usepackage[a4paper, total={7in, 10in}]{geometry}
\usepackage{graphicx}
\usepackage{hologo}
\usepackage{amssymb}
\usepackage{pgfplots}
\usepackage[inline]{enumitem}
\usepackage{amsmath}
\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{multienum} % weird with labels
\usetikzlibrary{calc} %% not really needed............. idk.
%\usetikzlibrary{external}
% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
%\tikzexternalize
\usepackage{xcolor}
\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}

\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}{Trikotnik }
\newcommand{\predmdn}{mat}
\newcommand{\stevilkadn}{11}
\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}}
}
\renewcommand\abstractname{Povzetek}
\date{19. oktober 2020}
\renewcommand\contentsname{Kazalo vsebine}
\renewcommand\figurename{Slika}
\renewcommand\abstractname{Povzetek}
\newcommand{\iic}{I\textsuperscript{2}C }
% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
\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}}


% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
\begin{document}
\maketitle

\begin{abstract}
Ta dokument obsega naloge, naročene dijakom 19. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učbenika. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno.
\end{abstract}
\tableofcontents

\section{Učbenik \textit{Matematika 2}: Trikotnik --- stran 33}
\begin{enumerate}[label=\textbf{\arabic*.}]
	\setcounter{enumi}{6}
	\item Načrtaj trikotnik s podatki: $c=\cm{4}, t_a=\cm{5,5}, \beta=\ang{120}$.
		\begin{center}
			\begin{tikzpicture}
				\tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B} \tkzDefPoint(5.5,0){AH}
				\tkzInterLC(A,B)(B,A) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(A,B)
				\tkzDrawLine(A,AX) \tkzLabelLine[above, pos = 0.25](A,AX){$c$}			\tkzCompass(B,AX) \tkzInterCC(B,AX)(AX,B) \tkzGetPoints{CH}{USELESS}
				\tkzCompass(B,CH) \tkzCompass(AX,CH)
				\tkzDrawLine(B,CH) \tkzLabelLine[above left](B,CH){$a$}
				\tkzInterLC(B,CH)(A,AH) \tkzGetPoints{HA}{USELESS}
				\tkzCompass(A,HA) \tkzInterLC(B,CH)(HA,B) \tkzGetPoints{BAGAIN}{C}
				\tkzCompass(HA,C) \tkzDrawLine(A,C) \tkzLabelLine[below](A,C){$b$}
				\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
			\end{tikzpicture}
		\end{center}
	\newpage
	\item Načrtaj trikotnike.
		\begin{multicols}{4}
			\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
				\item \color{codered} $$b=\cm{6}$$ $$v_b=\cm{4}$$ $$t_b=\cm{5}$$ % <&=&
				\item \color{black} $$a=\cm{5}$$ $$v_a=\cm{3,5}$$ $$\gamma=\ang{75}$$
				\item $$c=\cm{6}$$ $$a=\cm{4}$$ $$t_a=\cm{5,5}$$
				\item $$b=\cm{5,5}$$ $$t_c=\cm{5}$$ $$\alpha=\ang{60}$$
			\end{enumerate}
		\end{multicols}
		\begin{center}
			\begin{tikzpicture}
				\tkzDefPoint(0,0){A} \tkzDefPoint(69:6){C}
				\tkzDefPoint(69:4){VH} \tkzDefPoint(69:-2){TH}
				\tkzCompass(A,C) \tkzDrawLine(TH,C) \tkzLabelLine[below right](A,C){$b$}
				\tkzDefMidPoint(A,C) \tkzGetPoint{ACM}
				\tkzCompass(A,ACM) \tkzCompass(C,ACM)
				\tkzDefMidPoint(A,ACM) \tkzGetPoint{AACMM}
				\tkzInterLC(A,C)(A,AACMM) \tkzGetPoints{PH1}{PH2}
				\tkzCompass(A,PH1) \tkzCompass(A,PH2)
				\tkzInterCC(PH1,PH2)(PH2,PH1) \tkzGetPoints{USELESS}{V1}
				\tkzCompass(PH1,V1)\tkzCompass(PH2,V1)
				\tkzInterLC(A,V1)(A,VH) \tkzGetPoints{USELESS}{V}
				\tkzCompass(A,V) \tkzInterLC(A,V)(V,V1) \tkzGetPoints{USELESS}{V1X}
				\tkzDrawLine(A,V1X) \tkzCompass(V,V1X) \tkzInterCC(V1,V1X)(V1X,V1)
				\tkzGetPoints{VP}{VPX} \tkzCompass(V1,VP) \tkzCompass(V1X,VP)
				\tkzDrawLine(VPX,VP) \tkzInterLC(VP,VPX)(ACM,TH) \tkzGetPoints{USELE}{B}
				\tkzCompass(ACM,B) \tkzDrawLine(B,C) \tkzLabelLine[below left](B,C){$a$}
				\tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
				\tkzMarkRightAngles(PH1,A,V1 A,V,VP)
				\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
			\end{tikzpicture}
		\end{center}
	\item Načrtaj enakokraki trikotnik, katerega višina na osnovnico je dolga $\cm{3}$, kot ob osnovinci pa je velik $\ang{30}$.
		\begin{center}
			\begin{tikzpicture}
				\tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
				\tkzDrawLine(A,B) \tkzLabelLine[above,pos=.4](A,B){$c$} \tkzCompass(A,B)
				\tkzInterCC(A,B)(B,A) \tkzGetPoints{CL}{USELESS}
				\tkzCompass(A,B) \tkzCompass(A,CL)
				\tkzDefMidPoint(B,CL) \tkzGetPoint{K}\tkzCompass(B,K)\tkzCompass(CL,K)
				\tkzDrawLine(A,K)
				\tkzDefMidPoint(A,B) \tkzGetPoint{ABM} \tkzInterCC(A,B)(B,A)
				\tkzGetPoints{ABP}{ABPX} \tkzCompass(A,ABP) \tkzCompass(B,ABP)
				\tkzDrawLine(ABM,ABP) \tkzInterLL(ABPX,ABP)(A,K) \tkzGetPoint{C}
				\tkzLabelLine[above left](A,C){$b$}
				\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
				\tkzDrawPoints(A) \tkzLabelPoints(A)
				\tkzLabelPoint[below left](B){$B$} \tkzLabelPoint[above left](C){$C$}
			\end{tikzpicture}
		\end{center}
	\item Načrtaj pravokotni trikotnik s pravim kotom v oglišču $C$, katerega stranica $AC$ je dolga $\cm{4}$, simetrala kota pri $A$ pa $\cm{5}$. Nariši trikotniku včrtano krožnico.

	Na tem mestu naj povem, da je \textbf{simetrala kota poltrak} in nima dolžine!
	Zato trikotnika ne morem načrtati, zakar tudi včrtanje stranice ni možno. )-:
		\if\false1
			\begin{center}
				\begin{tikzpicture}
					\tkzDefPoint(0,0){A} \tkzDefPoint(69:4){C}
					\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
					\tkz
					\tkzDrawPoints(A) \tkzLabelPoints(A,C)
				\end{tikzpicture}
			\end{center}
		\fi
	\newpage
	\item Načrtaj trikotnik in trikotniku očrtano krožnico.
		\begin{multicols}{4}
			\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
				\item $$a=\cm{5}$$ $$b=\cm{4}$$ $$\alpha=\ang{75}$$
				\item \color{codered} $$b=\cm{3}$$ $$v_b=\cm{4}$$ $$\gamma=\ang{120}$$
				\item \color{black} $$a=\cm{4}$$ $$b=\cm{5}$$ $$\gamma=\ang{90}$$
				\item $$a=b=\cm{4}$$ $$c=6\cm$$
			\end{enumerate}
		\end{multicols}
		\begin{center}
			\begin{tikzpicture}
				\tkzDefPoint(0,0){A} \tkzDefPoint(69:3){C} \tkzDefPoint(69:4){VHX}
				\tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
				\tkzInterLC(A,C)(C,A) \tkzGetPoints{A}{AX}
				\tkzCompass(C,AX) \tkzDrawLine(A,AX) \tkzInterCC(AX,C)(C,AX)
				\tkzGetPoints{BH}{BHX} \tkzCompass(AX,BH) \tkzCompass(C,BH)
				\tkzDefMidPoint(A,C) \tkzGetPoint{ACM} \tkzCompass(A,ACM)
				\tkzInterLC(A,C)(A,ACM) \tkzGetPoints{ACMX}{ACM} \tkzCompass(A,ACMX)
				\tkzDrawLine(ACMX,AX)\tkzInterCC(ACMX,ACM)(ACM,ACMX) \tkzGetPoints{Y}{X}
				\tkzCompass(ACM,X) \tkzCompass(ACMX,X)
				\tkzInterLC(A,X)(A,VHX) \tkzGetPoints{USELESS}{VH}
				\tkzCompass(A,VH) \tkzInterLC(A,X)(VH,A) \tkzGetPoints{A}{AXX}
				\tkzCompass(VH,AXX) \tkzDrawLine(A,AXX)
				\tkzInterCC(A,AXX)(AXX,A) \tkzGetPoints{V2}{V2X}
				\tkzCompass(A,V2) \tkzCompass(AXX,V2) \tkzDrawLine(VH,V2)
				\tkzInterLL(V2,V2X)(C,BH) \tkzGetPoint{B} \tkzDrawLine(C,B)
				\tkzLabelLine[above left](C,B){$a$}
				\tkzDrawLine(A,B) \tkzLabelLine[above left](A,B){$c$}
				\tkzInterCC(C,B)(B,C) \tkzGetPoints{CBS}{CBSX} % krožnica
				\tkzCompass(C,CBS) \tkzCompass(B,CBS) \tkzDrawLine(CBS,CBSX)
				\tkzCompass(C,CBSX) \tkzCompass(B,CBSX)
				\tkzInterCC(A,B)(B,A) \tkzGetPoints{ABS}{ABSX}
				\tkzCompass(A,ABS) \tkzCompass(B,ABS) \tkzDrawLine(ABS,ABSX)
				\tkzCompass(A,ABSX) \tkzCompass(B,ABSX)
				\tkzInterLL(ABS,ABSX)(CBS,CBSX) \tkzGetPoint{S}
				\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
				\tkzMarkRightAngles(VH,A,C B,VH,A)
				\tkzDrawCircle[fill = red!30,opacity=.3](S,A)
				\tkzDrawPolygon[fill=blue!30,opacity=.3](A,B,C) % za razvidnost
			\end{tikzpicture}
		\end{center}
\end{enumerate}
 
\section{Zaključek}
Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
\hologo{LaTeX}
izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo mojem šolskem Git repozitoriju na
\url{https://github.com/sijanec/sola-gimb-2} v mapi 
\href{https://github.com/sijanec/sola-gimb-2/tree/master/\predmdn/domace_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je  \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/\predmdn/domace_naloge/\stevilkadn/dokument.pdf}.

\if\razhroscevanje1
\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: \input|"date -Ins"

Dokument se je generiral aaasecgeninsaaa sekund.
\fi
%	\item $$$$
\end{document}