Initial work

MA1006/tut-2023-10-10.tex

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+\input{decls.tex}
+\title{Tutorial 2023-10-10}
+\begin{document}
+\maketitle
+\section{}
+\section{}
+They're rotated by 90 degrees
+\section{}
+\begin{tabular}{ c c c c }
+$\theta$   & $\cos\theta$   & $\sin\theta$   & $\tan\theta$    \\ \hline
+$0$        & $ 1 $          & $ 0 $          & $ 0 $           \\ \hline
+$\pi/6$    & $\sqrt{3}/2$   & $1/2$          & $\sqrt{3}/3$    \\ \hline
+$\pi/4$    & $\sqrt{2}/2$   & $\sqrt{2}/2$   & $1$             \\ \hline
+$\pi/3$    & $1/2$          & $\sqrt{3}/2$   & $\sqrt{3}$      \\ \hline
+$\pi/2$    & $0$            & $1$            & undefined       \\ \hline
+$-\pi/6$   & $\sqrt{3}/2$   & $-1/2$         & $-\sqrt{3}/3$   \\ \hline
+$-\pi/4$   & $\sqrt{2}/2$   & $-\sqrt{2}/2$  & -1              \\ \hline
+$-\pi/3$   & $1/2$          & $-\sqrt{3}/2$  & $-\sqrt{3}$     \\ \hline
+$-\pi/2$   & $0$            & $-1$           & undefined       \\ \hline
+\end{tabular}
+\section{}
+\subsection{}
+\begin{align*}
+& +1 = \polar{1}{0} & {-1} = \polar{1}{\pi} \\
+& +i = \polar{1}{\frac{\pi}{2}} & {-i} = \polar{1}{-\frac{\pi}{2}}
+\end{align*}
+\subsection{}
+\[1 - i = \polar{\sqrt{2}}{\frac{-\pi}{4}}\]
+\[1 + i = \polar{\sqrt{2}}{\frac{\pi}{4}} \]
+\subsection{}
+\[-1 + i\sqrt{3} = \polar{2}{\frac{-\pi}{3}}\]
+\[-1 - i\sqrt{3} = \polar{2}{\frac{+\pi}{3}}\]
+\subsection{}
+\[\]
+\section{}
+\subsection{}
+\[i\]
+\subsection{}
+\[\sqrt{2} + \sqrt{2}i\]
+\subsection{}
+
+\end{document}