%
%	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
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\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。）
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\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
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% 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

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%\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
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% 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
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\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}
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\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

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



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

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\cos0^\circ$}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\sin90^\circ$}
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\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-1.5,-0.5) grid (1.5,2.05);
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%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\cos90^\circ$}
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\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-1.5,-0.5) grid (1.5,2.05);
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\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
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%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \cos 
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\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
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\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
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\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\tan90^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
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\draw(0.2,0.3) node {$\scriptstyle 90^\circ$};

\draw[->](-0.5,0)--(1,0) node[below right] {$\scriptstyle x$} 
			coordinate(x axis);
\draw[->](0,-0.5)--(0,2) node[left] {$\scriptstyle y$} 
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\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
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%\draw[help lines](-0.5,0) grid (6,6.2);
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		mark=between positions 0.4 and 0.6
		step 0.4 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=red,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-,CUDRed,ultra thin,line join=round] (0,-0.2) 
	..controls (1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[->,CUDRed,line width=3pt,line join=round] (0,-0.2)..controls
	(1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[CUDRed,line width=3pt,line join=round] (3.6,-0.2)..controls
	(3.1,0) and (3.2,0.2)..(3.2,1.9);
\draw[CUDRed,line width=3pt] (2.8,1.5)--(3.6,1.5);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\sin180^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-2.5,-0.5) grid (0.5,2.05);
\useasboundingbox(-2.5,-0.5) grid (0.5,2.05);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-1.7,0.3)--(-1.7,0);
\draw[fill,CUDRed] (0,0)--(-9pt,0) arc (180:170:9pt)--(0,0);
\draw[line width=1pt](0,0)--(-1.7,0.3);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
	(-0.2,0.2)--(-1.9,0.6)--(-1.9,0);
	}

\draw[->](9pt,0) arc (0:170:9pt);
\draw(0.5,0.3) node {$\scriptstyle 180^\circ$};
\draw(-0.8,0.05) node {$\scriptstyle 0^\circ$};

\draw[->](-2,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
				coordinate(x axis);
\draw[->](0,-0.5)--(0,2) node[left] {$\scriptstyle y$} 
				coordinate(y axis);

\fill[CUDRed](-1.7,0.3) circle (1pt);

\draw(-1.2,-0.2) node {$-1$};
\draw(-2,0.15) node {$0$};
\draw(-0.9,0.3) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \sin 
		= \myfrac{\text{縦}}{\,\text{斜め}\, } \)};}
\only<3->{\draw(0,2) node{\( \sin180^\circ =\myfrac{\,0\,}{1} \)};
	\draw(2.9,0) node{\( =0 \)\quad\□答};
	}

\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.8 and 1
		step 0.8 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=CUDRed,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-](0,0).. controls (1,0.3) and (2,1)..(3,2);
\draw[->,CUDRed,line width=3pt,line join=round] (0,0).. controls
	(1,0.3) and (2,1)..(3,2).. controls (3,0.5) and (3,-0.1)..(2.4,0);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\cos180^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-2.5,-0.5) grid (0.5,2.05);
\useasboundingbox(-2.5,-0.5) grid (0.5,2.05);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-1.7,0.3)--(-1.7,0);
\draw[fill,CUDRed] (0,0)--(-9pt,0) arc (180:170:9pt)--(0,0);
\draw[line width=1pt](0,0)--(-1.7,0.3);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
	(-1.5,0.4)--(0.5,-0.1)--(-1.5,-0.1);
	}

\draw[->](9pt,0) arc (0:170:9pt);
\draw(0.5,0.3) node {$\scriptstyle 180^\circ$};

%\draw[fill,CUDRed] (0,0)--(-9pt,0) arc (180:170:9pt) --(0,0);
\draw(-0.8,0.05) node {$\scriptstyle 0^\circ$};

\draw[->](-2,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
				coordinate(x axis);
\draw[->](0,-0.5)--(0,2) node[left] {$\scriptstyle y$} 
				coordinate(y axis);
\fill[CUDRed](-1.7,0.3) circle (1pt);

\draw(-1.2,-0.2) node {$-1$};
\draw(-2,0.15) node {$0$};
\draw(-0.9,0.3) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \cos 
		= \myfrac{\text{横}}{\,\text{斜め}\, } \)};}
\only<3->{\draw(0,2) node{\( \cos180^\circ =\myfrac{-1}{1} \)};
	\draw(2,0) node{\( =-1 \)\quad\□答};
	}

\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.4 and 0.6
		step 0.4 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=CUDRed,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-] (3,1.5)..controls (1,1.7) and (-0.2,0.5)..(0,0)
	..controls (0.2,-0.5) and (2,-0.5)..(3,-0.1);
\draw[->,CUDRed,line width=3pt,line join=round] (3,1.5)..controls
	(1,1.7) and (-0.2,0.5)..(0,0)
	..controls (0.2,-0.5) and (2,-0.5)..(3,-0.1);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\tan180^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-2.5,-0.5) grid (0.5,2.05);
\useasboundingbox(-2.5,-0.5) grid (0.5,2.05);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-1.7,0.3)--(-1.7,0);
\draw[fill,CUDRed] (0,0)--(-9pt,0) arc (180:170:9pt)--(0,0);
\draw[line width=1pt](0,0)--(-1.7,0.3);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
%	(0,-0.2)--(-1.8,-0.2)--(-1.8,0.3);
	(0,-0.3)--++(-1.8,0)--++(0,0.6);
	}

\draw[->](9pt,0) arc (0:170:9pt);
\draw(0.5,0.3) node {$\scriptstyle 180^\circ$};

%\draw[fill,CUDRed] (0,0)--(-9pt,0) arc (180:170:9pt) --(0,0);
\draw(-0.8,0.05) node {$\scriptstyle 0^\circ$};

\draw[->](-2,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
				coordinate(x axis);
\draw[->](0,-0.5)--(0,2) node[left] {$\scriptstyle y$} 
				coordinate(y axis);

\fill[CUDRed](-1.7,0.3) circle (1pt);

\draw(-1.2,-0.2) node {$-1$};
\draw(-2,0.15) node {$0$};
\draw(-0.9,0.3) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \tan= \myfrac{\text{縦}}{\,\text{横}\,} \)};}
\only<3->{\draw(0,2) node{\( \tan180^\circ = \myfrac{0}{-1} \)};
	\draw(3.1,0) node{\( =0 \)\quad\□答};
	}

\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.4 and 0.6
		step 0.4 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=red,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-,CUDRed,ultra thin,line join=round] (0,-0.2) 
	..controls (1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[->,CUDRed,line width=3pt,line join=round] (0,-0.2)..controls
	(1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[CUDRed,line width=3pt,line join=round] (3.6,-0.2)..controls
	(3.1,0) and (3.2,0.2)..(3.2,1.9);
\draw[CUDRed,line width=3pt] (2.8,1.5)--(3.6,1.5);
\end{scope}
\end{tikzpicture}

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

\begin{frame}[t]
\frametitle{$\sin270^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-1.5,-2.05) grid (1.5,0.5);
\useasboundingbox(-1.5,-2.05) grid (1.5,0.5);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-0.3,-1.7)--(-0.3,0);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
	(0.2,-0.2)--(-0.4,-2)--(-0.4,0);}

\draw[->](4pt,0) arc (0:260:4pt);
\draw(0.3,0.2) node {$\scriptstyle 270^\circ$};

\draw[->](-1,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
				coordinate(x axis);
\draw[->](0,-2)--(0,0.5) node[left] {$\scriptstyle y$} 
				coordinate(y axis);

\fill[CUDRed](-0.3,-1.7) circle (1pt);

\draw(-0.15,0.2) node {$0$};
\draw(-0.6,-0.8) node {$-1$};
\draw(-0.1,-1.2) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \sin 
		= \myfrac{\text{縦}}{\,\text{斜め}\, } \)};}
\only<3->{\draw(0,2) node{\( \sin270^\circ =\myfrac{-1}{1} \)};
	\draw(2,0) node{\( =-1 \)\quad\□答};
	}

\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.8 and 1
		step 0.8 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=CUDRed,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-](0,0).. controls (1,0.3) and (2,1)..(3,2);
\draw[->,CUDRed,line width=3pt,line join=round] (0,0).. controls
	(1,0.3) and (2,1)..(3,2).. controls (3,0.5) and (3,-0.1)..(2.4,0);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\cos270^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-1.5,-2.05) grid (1.5,0.5);
\useasboundingbox(-1.5,-2.05) grid (1.5,0.5);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-0.3,-1.7)--(-0.3,0);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
	(-0.2,-2)--(0.2,0.2)--(-0.4,0.2);}

\draw[->](4pt,0) arc (0:260:4pt);
\draw(0.3,0.2) node {$\scriptstyle 270^\circ$};

\draw[->](-1,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
		coordinate(x axis);
\draw[->](0,-2)--(0,0.5) node[left] {$\scriptstyle y$} 
		coordinate(y axis);

\fill[CUDRed](-0.3,-1.7) circle (1pt);

\draw(-0.15,0.2) node {$0$};
\draw(-0.6,-0.8) node {$-1$};
\draw(-0.1,-1.2) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \cos 
		= \myfrac{\text{横}}{\,\text{斜め}\, } \)};}
\only<3->{\draw(0,2) node{\( \cos270^\circ =\myfrac{\,0\,}{1} \)};
	\draw(2.1,0) node{\( =0 \)\quad\□答};
	}
\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.4 and 0.6
		step 0.4 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=CUDRed,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-] (3,1.5)..controls (1,1.7) and (-0.2,0.5)..(0,0)
	..controls (0.2,-0.5) and (2,-0.5)..(3,-0.1);
\draw[->,CUDRed,line width=3pt,line join=round] (3,1.5)..controls
	(1,1.7) and (-0.2,0.5)..(0,0)
	..controls (0.2,-0.5) and (2,-0.5)..(3,-0.1);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\tan270^\circ$}
\vspace*{-1ex}
\begin{tikzpicture}[thick,scale=2.5,>=stealth]
%\draw[help lines](-1.5,-2.05) grid (1.5,0.5);
\useasboundingbox(-1.5,-2.05) grid (1.5,0.5);
\filldraw[fill=CUDLime,draw=black,line width=1pt](0,0)--(-0.3,-1.7)--(-0.3,0);
\visible<2->{\draw[->,line width=5pt,rounded corners=8pt,CUDBlue]
	(0,0.2)--(-0.4,0.2)--(-0.4,-2);
	}

\draw[->](4pt,0) arc (0:260:4pt);
\draw(0.3,0.2) node {$\scriptstyle 270^\circ$};

\draw[->](-1,0)--(0.5,0) node[below right] {$\scriptstyle x$} 
				coordinate(x axis);
\draw[->](0,-2)--(0,0.5) node[left] {$\scriptstyle y$} 
				coordinate(y axis);

\fill[CUDRed](-0.3,-1.7) circle (1pt);

\draw(-0.15,0.2) node {$0$};
\draw(-0.6,-0.8) node {$-1$};
\draw(-0.1,-1.2) node {$1$};
\end{tikzpicture}
\begin{tikzpicture}[rotate=0, scale=1,right,anchor=base west,
	baseline={([yshift=-20ex] current bounding box.north)}]
%\draw[help lines](-0.5,0) grid (6,6.2);
\useasboundingbox(-0.5,0) grid (6,6.2);
\only<1-2>{\draw(0,2) node{\( \tan= \myfrac{\text{縦}}{\,\text{横}\,} \)};}
\only<3->{\draw(0,2) node{\( \tan270^\circ = \myfrac{-1}{0} \)};
	\draw(1,0) node{\( =\text{値なし} \)\quad\□答};
	}

\begin{scope}[yshift=12ex,>=stealth, ->-/.style = {decoration={markings,
		mark=between positions 0.4 and 0.6
		step 0.4 with {\arrow{Stealth[length=1.4ex]}}},
              postaction={decorate},draw=red,ultra thin,line join=round}]% 筆記体を書く
\draw[line width=1.5pt,rounded corners=1pt](0.5,0)--(2.5,1.2)--(2.5,0)--cycle;
\draw[line width=1pt](2.3,0.2) rectangle (2.5,0);
\draw[->-,CUDRed,ultra thin,line join=round] (0,-0.2) 
	..controls (1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[->,CUDRed,line width=3pt,line join=round] (0,-0.2)..controls
	(1,-0.2) and (3.2,-0.5)..(3.2,0.3)
	..controls (3.2,0.7) and (3.2,1.5)..(3.2,2);
\draw[CUDRed,line width=3pt,line join=round] (3.6,-0.2)..controls
	(3.1,0) and (3.2,0.2)..(3.2,1.9);
\draw[CUDRed,line width=3pt] (2.8,1.5)--(3.6,1.5);
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}

