alientrig.tex

\RequirePackage{luatex85}
\documentclass{amsart}
\usepackage[a6paper, margin=0.2in, landscape]{geometry}
\begin{document}
\thispagestyle{empty}
\renewcommand\sqrt{\,\text{sqrt}}
\centering
$\begin{aligned}
&\theta \qquad 	&&\theta\tau\sin &&\theta\tau\cos &&\theta\tau\tan
\\[1ex] \hline \\[-1.5ex]
&0		&&0			&&1			&&0 \\
&0.1		&&0.6		&&0.9 \sqrt	&&0.4\sqrt \\
&0.16	&&0.6 \sqrt	&&0.6 \sqrt	&&1 \\
&0.2		&&0.9 \sqrt	&&0.6		&&3\sqrt \\
&0.3		&&1			&&0			&&\infty \\
&0.4		&&0.9 \sqrt	&&0.6-		&&3\sqrt- \\
&0.46	&&0.6 \sqrt	&&0.6 \sqrt-	&&1- \\
&0.5		&&0.6		&&0.9 \sqrt-	&&0.4\sqrt- \\
&0.6		&&0			&&1-			&&0 \\
&0.7		&&0.6-		&&0.9 \sqrt-	&&0.4\sqrt \\
&0.76	&&0.6 \sqrt-	&&0.6 \sqrt-	&&1 \\
&0.8		&&0.9 \sqrt-	&&0.6-		&&3\sqrt \\
&0.9		&&1- 		&&0			&&\infty \\
&0.t		&&0.9 \sqrt- 	&&0.6		&&3\sqrt- \\
&0.t6		&&0.6 \sqrt- 	&&0.6 \sqrt	&&1- \\
&0.e		&&0.6- 		&&0.9 \sqrt 	&&0.4\sqrt- \\
&1.0		&&0 			&&1			&&0
\end{aligned}
\quad
\begin{aligned}
&\theta\tau\csc &&\theta\tau\sec &&\theta\tau\cot
\\[1ex] \hline \\[-1.5ex]
&\infty		&&1			&&\infty \\
&2			&&1.4 \sqrt	&&3\sqrt \\
&2 \sqrt		&&2 \sqrt		&&1 \\
&1.4 \sqrt		&&2			&&0.4\sqrt \\
&1			&&\infty		&&0 \\
&1.4 \sqrt		&&2-			&&0.4\sqrt- \\
&2 \sqrt		&&2 \sqrt-		&&1- \\
&2			&&1.4 \sqrt-	&&3\sqrt- \\
&\infty		&&1-			&&\infty \\
&2-			&&1.4 \sqrt-	&&3\sqrt \\
&2 \sqrt- 		&&2 \sqrt-		&&1 \\
&1.4 \sqrt- 	&&2-			&&1.4\sqrt \\
&1- 			&&\infty		&&0 \\
&1.4 \sqrt- 	&&2			&&0.4\sqrt- \\
&2 \sqrt- 		&&2 \sqrt		&&1- \\
&2- 			&&1.4 \sqrt 	&&3\sqrt- \\
&\infty 		&&1			&&\infty
\end{aligned}$
\end{document}

\newpage
$~$\vspace{1in}
\begin{align*}
(\theta \tan^2+1)\sqrt\,\text{inv}- :=
(\theta \tan^2+1)^{0.6-} &= \theta \cos \text{abs} \\
(\theta \tan^{2-}+1)^{0.6-} &= \theta \sin \text{abs} \\
\theta \cos &= (\theta i) \, \exp \, \text{Re} := \theta \text{ cis Re}
 \\
\theta \sin &= (\theta i) \, \exp \, \text{Im}
\end{align*}