\documentclass[a4paper]{article}
\usepackage{german}
\usepackage[utf8]{inputenc}

\usepackage{pgfplots}

\usepackage{pgfplotstable}
\usepackage{booktabs}
\usepackage{array}
\usepackage{colortbl}

\begin{document}
\iffalse
\begin{tikzpicture}
%\tracingcommands=2\tracingmacros=2
	\begin{axis}
		\addplot [domain=15:30, samples=1000] {4*65*sin(0.25*asin(x/65))/x};
	\end{axis}
\end{tikzpicture}
\fi

\makeatletter

\def\result#1#2{\def\pgfmathresult{#1}}

\long\def\test#1#2#3{%
	%
	#3{#2}%
	\let\expected=\pgfmathresult
	%
	#1(#2) : actual \csname pgfmath#1@\endcsname{#2}\pgfmathresult. expected \expected.
	%
	\pgfmathfloatparsenumber\pgfmathresult
	\let\actual=\pgfmathresult
	\pgfmathfloatparsenumber{\expected}%
	\let\expected=\pgfmathresult
	\pgfmathfloatrelerror{\actual}{\expected}%
	Error: 
	\pgfmathprintnumber\pgfmathresult
	\par
}%

\test{asin}{0.31}{\result{18.0592304907836}}

\test{asin}{0.31023}{\result{18.0730919007721}}

\test{asin}{0.31046}{\result{18.0869544051815}}

\test{asin}{1}{\result{90.0}}


\test{acos}{0.31}{\result{71.9407695092165}}

\test{acos}{0.31023}{\result{71.9269080992279}}

\test{acos}{0.31046}{\result{71.9130455948185}}

\test{acos}{1}{\result{0.0}}



\def\pgfmathlua#1{%
	\edef\pgfmathresult{\directlua{tex.print(math.sin(#1*2*math.pi/360))}}%
}%
\test{sin}{3.335453000000000}{\pgfmathlua}
\test{sin}{3.3388405000000000}{\pgfmathlua}
\test{sin}{3.342228000000000}{\pgfmathlua}
\test{sin}{3.3457603000000000}{\pgfmathlua}
\test{sin}{3.3491478000000000}{\pgfmathlua}
\test{sin}{3.3525352000000000}{\pgfmathlua}
\test{sin}{3.3559189000000000}{\pgfmathlua}
\test{sin}{3.3593063000000000}{\pgfmathlua}
\test{sin}{3.3625488000000000}{\pgfmathlua}
\test{sin}{3.3659325000000000}{\pgfmathlua}
\test{sin}{3.3696136000000000}{\pgfmathlua}
\end{document}

