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-rw-r--r-- | buch/chapters/030-geometrie/images/einheitskreis.tex | 86 |
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diff --git a/buch/chapters/030-geometrie/images/einheitskreis.tex b/buch/chapters/030-geometrie/images/einheitskreis.tex new file mode 100644 index 0000000..c38dc19 --- /dev/null +++ b/buch/chapters/030-geometrie/images/einheitskreis.tex @@ -0,0 +1,86 @@ +% +% einheitskreis.tex -- trigonometrische Funktionen und Einheitskreis +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\a{33} +\def\b{142} +\def\r{3} +\def\R{2} +\draw[color=red,line width=1.4pt] (0,0) circle[radius=\r]; + +\fill[color=darkgreen!10] (0,0) -- ({\r*cos(\b)},0) -- (\b:\r) -- cycle; +\node[color=darkgreen] at ({\b+0.5*(180-\b)}:{0.6*\r}) {$\Delta$}; +\fill[color=darkgreen!20] (0,0) -- (0:{0.6*\R}) arc (0:\b:{0.6*\R}) -- cycle; +\node[color=darkgreen] at ({0.5*\b}:{0.4*\R}) {$\beta$}; + +\fill[color=blue!20,opacity=0.5] (0,0) -- ({\r*cos(\a)},0) -- (\a:\r) -- cycle; +\fill[color=blue!40,opacity=0.5] (0,0) -- (0:{0.45*\R}) arc (0:\a:{0.45*\R}) -- cycle; +\node[color=blue] at ({0.5*\a}:{0.3*\R}) {$\alpha$}; +\node[color=blue] at ({0.5*\a}:{0.6*\r}) {$\Delta$}; + +\node[color=blue] at ($(\a:\r)+(0.1,0)$) [above] {$P$}; +\node[color=darkgreen] at ($(\b:\r)+(-0.05,-0.05)$) [left] {$Q$}; + +\begin{scope} +\clip (-5,-4) rectangle (5,4); +\draw[color=blue,line width=1.0pt] (0,0) -- (\a:\r); +\draw[color=blue,line width=0.4pt] (\a:\r) -- (\a:10); +\fill[color=blue] (\a:\r) circle[radius=0.05]; + +\draw[color=blue,line width=1.4pt] (\r,0) -- (\r,{\r*tan(\a)}); +\node[color=blue] at (\r,{0.5*\r*tan(\a)}) [right] {$\tan\alpha$}; + +\draw[color=blue,line width=0.4pt] ({\r*cos(\a)},0) -- (\a:\r); +\node[color=blue] at ({\r*cos(\a)},0) [below] {$\cos\alpha\mathstrut$}; +\draw[color=blue] ({\r*cos(\a)},-0.1) -- ({\r*cos(\a)},0.1); + +\draw[color=blue,line width=0.4pt] (0,{\r*sin(\a)}) -- (\a:\r); +\node[color=blue] at (0.05,{\r*sin(\a)+0.1}) + [below left] {$\sin\alpha\mathstrut$}; +\draw[color=blue] (-0.1,{\r*sin(\a)}) -- (0.1,{\r*sin(\a)}); + +\draw[color=blue,line width=1.4pt] (0,\r) -- ({\r/tan(\a)},\r); +\node[color=blue] at ({0.5*\r/tan(\a)},\r) [above] {$\cot\alpha$}; + +\draw[color=darkgreen,line width=1pt] (0,0) -- (\b:\r); +\draw[color=darkgreen,line width=0.4pt] (\b:\r) -- (\b:10); +\draw[color=darkgreen,line width=0.4pt] (0,0) -- (\b:-10); +\fill[color=darkgreen] (\b:\r) circle[radius=0.05]; + +\draw[color=darkgreen,line width=1.4pt] (0,\r) -- ({\r/tan(\b)},\r); +\node[color=darkgreen] at ({0.5*\r/tan(\b)},\r) [above] {$\cot\beta$}; + +\draw[color=darkgreen,line width=1.4pt] (\r,0) -- (\r,{\r*tan(\b)}); +\node[color=darkgreen] at (\r,{0.5*\r*tan(\b)}) [right] {$\tan\beta$}; + +\draw[color=darkgreen,line width=0.4pt] (\b:\r) -- (0,{\r*sin(\b)}); +\node[color=darkgreen] at (-0.05,{\r*sin(\b)-0.1}) + [above right] {$\sin \beta\mathstrut$}; +\draw[color=darkgreen] (-0.1,{\r*sin(\b)}) -- (0.1,{\r*sin(\b)}); + +\draw[color=darkgreen,line width=0.4pt] (\b:\r) -- ({\r*cos(\b)},0); +\node[color=darkgreen] at ({\r*cos(\b)},0) [below] {$\cos\beta\mathstrut$}; +\draw[color=darkgreen] ({\r*cos(\b)},-0.1) -- ({\r*cos(\b)},0.1); + +\end{scope} + +\draw[->] (-5.1,0) -- (5.4,0) coordinate[label={$x$}]; +\draw[->] (0,-4.1) -- (0,4.4) coordinate[label={right:$y$}]; +\node at (0,0) [below left] {$O$}; + +\end{tikzpicture} +\end{document} + |