%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
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% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
%\usetikzlibrary{calc}
%\usetikzlibrary{arrows.meta,patterns,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=5mm,text margin right=5mm}
\fboxrule=0.8pt

\makeatletter
\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
%\setbeamercolor{palette primary}{bg=CUDOrange}
%\setbeamercolor{frametitle}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{palette primary}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{frametitle}{bg=CUDCream!75,fg=black!80}
%\setbeamercolor{palette primary}{bg=CUDCream!75,fg=black!80}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}

\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=0pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu%■default
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
%\medmuskip=4mu plus 2mu minus 4mu%■default
\medmuskip=1mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu%■default
\thickmuskip=2mu plus 2mu minus 2mu
% mu は math units の省略で長さの単位

\newcommand{\slashup}[3]{\setbox0=\hbox{#1}
	#1\tikz[baseline=0pt]{\useasboundingbox(0,0);%縦0横0の描画領域
		\draw[#3,line width=0.2ex]
			(0, -\the\dp0)--++(-\the\wd0, \the\ht0+\the\dp0);
		\draw(-\the\wd0/2,2.4ex) node{\small\(#2\)};}
	}
\newcommand{\slashdown}[3]{\setbox0=\hbox{#1}
	#1\tikz[baseline=0pt]{\useasboundingbox(0,0);
		\draw[#3,line width=0.2ex]
			(0, -\the\dp0)--++(-\the\wd0, \the\ht0+\the\dp0);
		\draw(-\the\wd0/2,-1.2ex) node{\small\(#2\)};}
	}

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{正弦定理（外接円の半径\(R\)）}
\centerline{%
\begin{minipage}{0.7\textwidth}
\begin{beamercolorbox}[wd=\textwidth,ht=4ex,dp=3ex,shadow=true,
	rounded=true, center]{CUDCream}
\( \myfrac{a}{\sin A} =\myfrac{b}{\sin B} =\myfrac{c}{\sin C} =2R \)
\tikz[baseline=0pt]{\useasboundingbox(0,0);
		\draw[CUDBlue,line width=0.3ex]
			(-5.2em,-2.4ex) rectangle ++(5.4em,6ex)
			node[midway,yshift=-5ex]{\small 今回はココです};
		}
\end{beamercolorbox}
\end{minipage}
}

\vskip3ex
\[ (R \text{は外接円の半径}) \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{正弦定理（外接円の半径\(R\)）}
こっちの方がいいと思うよ

\bigskip
\centerline{%
\begin{minipage}{0.7\textwidth}
\begin{beamercolorbox}[wd=\textwidth,ht=4ex,dp=3ex,shadow=true,
	rounded=true, center]{CUDCream}
\( \myfrac{\ \text{\textcolor{CUDRed}{角度の向かいの辺}}\ }{
	\sin\text{\textcolor{CUDRed}{角度}}} = 2R \)
\end{beamercolorbox}
\end{minipage}
}

\bigskip
%\centerline{（ただし\(R\)は外接円の半径）}
\[ (\text{ただし}R \text{は外接円の半径}) \]

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$1$）}
\begin{tikzpicture}[scale=2, >=stealth, thick,
	baseline={([yshift=-24pt] current bounding box.north)}]
\coordinate (O) at (0,0);
\coordinate (C) at (-60:1.6);
\coordinate (B) at (-120:1.6);
\coordinate (A) at (110:1.6);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\fill[CUDRed] (A) circle (5mm);
\end{scope}

\alt<3->{\draw[dashed](A) ++(4pt,-25pt)
	node[circle,draw=CUDGreen,solid,ultra thick, inner sep=3pt](kakudo)
	{\footnotesize $30^\circ$};
	\draw[dashed](B) to[out=30,in=150] node[fill=white,inner sep=6pt,
		draw=CUDGreen,solid,ultra thick,circle](nagasa)
			{\footnotesize\( 4 \)} (C);
		}{\draw(A) ++(4pt,-25pt) node(kakudo)
			{\footnotesize $30^\circ$};
	\draw[dashed](B) to[out=30,in=150] node[fill=white,inner sep=3pt]
		(nagasa){\footnotesize\( 4 \)} (C);
	}
\draw[line join=round] (A)--(B)--(C)--cycle;
\visible<2->{\draw(O) circle (1.6);
	\draw(-0.3,0) node{\small \(O\)};
	\draw[dashed, CUDBlue, ultra thick](O) -- (B);
	\draw(-140:0.7) node[CUDBlue]{\footnotesize $R$};
	\fill (O) circle (1.5pt);
	}
\visible<3->{\draw[CUDGreen, ->, line width=8pt](kakudo)
	to[out=-60,in=80] (nagasa);
	}
\end{tikzpicture}
\begin{minipage}[t]{0.5\textwidth}
\visible<4->{\[ \myfrac{\textcolor{CUDGreen}{4} }{
		\sin \textcolor{CUDGreen}{30^\circ}}=2R \]

	\bigskip
	\hfill から\textcolor{CUDRed}{スタート！}
	}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$1$）}
\vspace*{-4.8ex}
\begin{eqnarray*}
\myfrac{4}{\sin 30^\circ} &=& 
	\alt<2->{\textcolor{CUDBlue}{2}R}{2R} \quad\pause
	\colorbox{CUDCream}{\footnotesize
		$R$を求めるには\textcolor{CUDBlue}{$2$}が邪魔}\\[2ex]\pause
\textcolor{CUDRed}{\myfrac{\,1\,}{\slashdown{2}{}{CUDGreen}}\times}
	\myfrac{\slashup{4}{2}{CUDGreen}}{\sin 30^\circ}
	&=& \textcolor{CUDBlue}{2}R 
		\textcolor{CUDRed}{\times\myfrac{\,1\,}{2}} \\[1ex]\pause
\hooklen{\myfrac{\,1\,}{2}\times\myfrac{4}{\sin 30^\circ}}
		{\myfrac{2}{\sin 30^\circ}}
	&=& \hooklen{2R\times\myfrac{\,1\,}{2}}{R} \\[1ex]\pause
2 \div \sin 30^\circ &=& \hooklen{2R\times\myfrac{\,1\,}{2}}{R}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$1$）}
\vspace*{-5ex}
\begin{eqnarray*}
\visible<2->{%
\begin{tikzpicture}[scale=0.8, thick,
	baseline={([yshift=-3ex] current bounding box.north)}]
\fill[CUDCream](-1,-0.3) rectangle (2.8,1.2);
\draw[text=CUDRed,rounded corners=.3pt](0,0)--
	node[pos=0.6,fill=white,inner sep=1pt]{\tiny$\sqrt{3}$}
	({sqrt(3)},0)-- node[fill=white,inner sep=1pt,xshift=6pt]{\tiny$1$}
	({sqrt(3)},1)-- 
	node[fill=white,inner sep=1pt,xshift=-6pt,yshift=4pt]{\tiny$2$}
							cycle;
\draw(12pt,0) arc [start angle=0, end angle=30,radius=12pt];
\draw(-10pt,6pt) node{\tiny\( 30^\circ \)};
\end{tikzpicture}
} \quad
2 \div \sin 30^\circ &=& R \hspace*{0.36\textwidth}\\[1ex]\pause\pause
2 \div \hooklen{\sin 30^\circ}{%
	\myfrac{\,\textcolor{CUDRed}{1}\,}{\textcolor{CUDRed}{2}}}
		&=& R \\[1ex]\pause
2 \textcolor{CUDBlue}{\times}
	\hooklen{\sin 30^\circ}{\textcolor{CUDBlue}{\myfrac{\,2\,}{1}}}
	&=& R \\[1ex]\pause
\text{\□答}\quad 4 \qquad &=& R
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$2$）}
\begin{tikzpicture}[scale=2, >=stealth, thick,
	baseline={([yshift=-24pt] current bounding box.north)}]
\coordinate (O) at (0,0);
\coordinate (C) at (100:1.6);
\coordinate (B) at (-20:1.6);
\coordinate (A) at (-160:1.6);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\fill[CUDRed] (A) circle (3mm);
\end{scope}
\draw[line join=round] (A)--(B)--(C)--cycle;
\alt<3->{\draw[dashed](A)++(16pt,6pt) node[circle,draw=CUDGreen,solid,
		ultra thick,inner sep=3pt](kakudo){\footnotesize $60^\circ$};
	\draw[dashed](B) to[out=170,in=-90] node[fill=white, inner sep=6pt,
		draw=CUDGreen,solid,ultra thick,circle]
		{\footnotesize\( 6 \)} (C);
	}{\draw(A) ++(16pt,6pt) node(kakudo){\footnotesize $60^\circ$};
		\draw[dashed](B) to[out=170,in=-90] node[fill=white,
			inner sep=3pt](nagasa){\footnotesize\( 6 \)} (C);
	}
\visible<3->{\draw[CUDGreen, ->, line width=8pt](kakudo) 
		to[out=60,in=180] (nagasa);}
\visible<2->{\draw (O) circle (1.6);
	\draw[dashed, CUDBlue, ultra thick](O)--(0,-1.6);
	\draw(-100:1) node[CUDBlue]{\footnotesize $R$};
	\fill (O) circle (1pt);
	}
\end{tikzpicture}
\begin{minipage}[t]{0.5\textwidth}
\visible<4->{\[ \myfrac{\textcolor{CUDGreen}{6}}{
	\sin \textcolor{CUDGreen}{60^\circ}}=2R \]

	\bigskip
	\hfill から\textcolor{CUDRed}{スタート！}
	}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$2$）}
\vspace*{-4.8ex}
\begin{eqnarray*}
\myfrac{6}{\sin 60^\circ} &=& \alt<2->{\textcolor{CUDBlue}{2}R}{2R}
			\quad\pause
	\colorbox{CUDCream}{\footnotesize
		$R$を求めるには\textcolor{CUDBlue}{$2$}が邪魔}\\[2ex]\pause
\textcolor{CUDRed}{\myfrac{\,1\,}{\slashdown{2}{}{CUDGreen}}\times}
		\myfrac{\slashup{6}{3}{CUDGreen}}{\sin 60^\circ}
	&=& \textcolor{CUDBlue}{2}R 
		\textcolor{CUDRed}{\times\myfrac{\,1\,}{2}} \\[1ex]\pause
\hooklen{\myfrac{\,1\,}{2}\times\myfrac{6}{\sin 60^\circ}}
		{\myfrac{3}{\sin 60^\circ}}
	&=& \hooklen{2R\times\myfrac{\,1\,}{2}}{R} \\[1ex]\pause
3 \div \sin 60^\circ &=& \hooklen{2R\times\myfrac{\,1\,}{2}}{R}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$2$）}
\vspace*{-4.8ex}
\begin{eqnarray*}
\visible<2->{%
\begin{tikzpicture}[scale=0.8, thick,
	baseline={([yshift=-3.5ex] current bounding box.north)}]
\fill[CUDCream](-1,-0.3) rectangle (1.8,1.8);
\draw[text=CUDRed,rounded corners=.3pt](0,0)-- 
		node[pos=0.6,fill=white,inner sep=1pt]{\tiny$1$}
	(1,0)-- node[xshift=6pt,fill=white,inner sep=1pt]{\tiny$\sqrt{3}$}
	(1,{sqrt(3)})-- node[fill=white,inner sep=1pt,xshift=-1ex]{\tiny$2$}
							cycle;
\draw(8pt,0) arc [start angle=0, end angle=60,radius=8pt];
\draw(-10pt,6pt) node{\tiny\( 60^\circ \)};
\end{tikzpicture}
} \quad
3 \div \sin 60^\circ &=& R \hspace*{0.2\textwidth}\\[-1ex]\pause\pause
3 \div \hooklen{\sin 60^\circ}{%
	\myfrac{\ \textcolor{CUDRed}{\sqrt{3}}\ }{\textcolor{CUDRed}{2}}}
			&=& R \\\pause
3 \textcolor{CUDBlue}{\times} 
	\hooklen{\sin 60^\circ}{\textcolor{CUDBlue}{\myfrac{2}{\ \sqrt{3}\ }}}
				&=& R \\\pause
\hooklen{3 \div \sin 60^\circ}{\myfrac{6}{\ \sqrt{3}\ }} &=& R
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{外接円の半径\(R\)を求めなさい（その$2$）}
\vspace*{-5ex}
\begin{eqnarray*}
\myfrac{6}{\ \sqrt{3}\ } \quad &=& R \pause\qquad
	\colorbox{CUDCream}{\footnotesize 有理化する}\\ \pause
\myfrac{6 \text{\textcolor{CUDRed}{\(\scriptstyle\times\sqrt{3}\)}}
}{\sqrt{3}\text{\textcolor{CUDRed}{\(\scriptstyle\times\sqrt{3}\)}}}
	&=& R \pause\qquad
	\colorbox{CUDCream}{\footnotesize\( \sqrt{3}\times\sqrt{3}=3 \)}\\ 
								\pause
\myfrac{\ 6\sqrt{3}\ }{3} &=& R \\ \pause
\text{\□答}\quad 2\sqrt{3} &=& R
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\end{document}

