42 lines
1.4 KiB
TeX
42 lines
1.4 KiB
TeX
\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} |