$\begingroup$ @robjohn: OK fair enough, I wasn't really trying to define sine and cosine so much as I was trying to point out that radians are usually introduced via the arclength of a wedge, not the area of a wedge (divided by 2). Also, I didn't have a problem with using that...
\documentclass[12pt]{scrartcl} \usepackage[latex, shellescape]{gmp} \gmpoptions{everymp={input latexmp; setupLaTeXMP(options="12pt", textextlabel=enable, mode=rerun);}} \begin{document} \begin{mpost*}[mpmem=metafun] % Macro that finds all points of p where the tangents share the ...
How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution. This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, ...