Add Unit 5

Author: Kayzels

notes.tex

@@ -18,4 +18,5 @@
 	\addfile{units/unit02.tex}
 	\addfile{units/unit03.tex}
 	\addfile{units/unit04.tex}
+	\addfile{units/unit05.tex}
 \end{document}

units/unit04.tex

@@ -162,6 +162,5 @@
 						\end{align*}
 				\end{enumerate}
 			\end{example}
-	\ifSubfilesClassLoaded{%
-		\vbox{\rulechapterend}}{\vspace*{\parskip}\rulebookend}
+			\rulechapterend
 \end{document}

units/unit05.tex

@@ -0,0 +1,104 @@
+\providecommand{\main}{..}
+\documentclass[\main/notes.tex]{subfiles}
+
+\begin{document}
+	\setcounter{chapter}{4}
+	\chapter{Trigonometry}
+		\section{Special Angles}
+		\begin{center}
+			\begin{tikzpicture}[scale=5,cap=round,>=latex]
+				% draw the coordinates
+				\draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$};
+				\draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$};
+
+				% draw the unit circle
+				\draw[thick] (0cm,0cm) circle(1cm);
+
+				\foreach \x in {0,30,...,360} {
+					% lines from center to point
+					\draw[gray] (0cm,0cm) -- (\x:1cm);
+					% dots at each point
+					\filldraw[black] (\x:1cm) circle(0.4pt);
+					% draw each angle in degrees
+					\draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
+				}
+
+				% draw each angle in radians
+				\foreach \x/\xtext in {
+					30/\frac{\pi}{6},
+					45/\frac{\pi}{4},
+					60/\frac{\pi}{3},
+					90/\frac{\pi}{2},
+					120/\frac{2\pi}{3},
+					135/\frac{3\pi}{4},
+					150/\frac{5\pi}{6},
+					180/\pi,
+					210/\frac{7\pi}{6},
+					225/\frac{5\pi}{4},
+					240/\frac{4\pi}{3},
+					270/\frac{3\pi}{2},
+					300/\frac{5\pi}{3},
+					315/\frac{7\pi}{4},
+					330/\frac{11\pi}{6},
+					360/2\pi}
+						\draw (\x:0.85cm) node[fill=white] {$\xtext$};
+
+				\foreach \x/\xtext/\y in {
+					% the coordinates for the first quadrant
+					30/\sqrt{3}/1,
+					45/\sqrt{2}/\sqrt{2},
+					60/1/\sqrt{3},
+					% the coordinates for the second quadrant
+					150/-\sqrt{3}/1,
+					135/-\sqrt{2}/\sqrt{2},
+					120/-1/\sqrt{3},
+					% the coordinates for the third quadrant
+					210/-\sqrt{3}/-1,
+					225/-\sqrt{2}/-\sqrt{2},
+					240/-1/-\sqrt{3},
+					% the coordinates for the fourth quadrant
+					330/\sqrt{3}/-1,
+					315/\sqrt{2}/-\sqrt{2},
+					300/1/-\sqrt{3}}
+						\draw (\x:1.25cm) node[fill=white] {$\left(\xtext,\y\right)$};
+
+				% draw the horizontal and vertical coordinates
+				% the placement is better this way
+				\draw (-1.25cm,0cm) node[above=1pt] {$(-2,0)$}
+					(1.25cm,0cm)  node[above=1pt] {$(2,0)$}
+					(0cm,-1.25cm) node[fill=white] {$(0,-2)$}
+					(0cm,1.25cm)  node[fill=white] {$(0,2)$};
+			\end{tikzpicture}
+		\end{center}
+	\section{Identities}
+		\subsection{Defining Relations}
+			\begin{alignat*}{2}
+				\tan \theta &= \frac{\sin\theta}{\cos\theta} \qquad & \cot \theta &= \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}\\
+				\sec\theta &= \frac{1}{\cos\theta} \qquad & \csc\theta &= \frac{1}{\sin\theta}
+			\end{alignat*}
+		\subsection{Pythagorean Identity}
+			\begin{align*}
+				\sin^{2}\theta + \cos^{2}\theta = 1
+			\end{align*}
+		\subsection{Negative Angles}
+			\begin{alignat*}{3}
+				\sin(-\theta) &= -\sin\theta \qquad & \cos(-\theta) &= \cos\theta \qquad & \tan(-\theta) = -\tan\theta
+			\end{alignat*}
+		\subsection{Sum and Difference}
+			\begin{alignat*}{2}
+				\sin(\alpha + \beta) &= \sin\alpha\cos\beta + \cos\alpha\sin\beta \qquad &
+				\sin(\alpha - \beta) &= \sin\alpha\cos\beta - \cos\alpha\sin\beta\\
+				\cos(\alpha + \beta) &= \cos\alpha\cos\beta - \sin\alpha\sin\beta
+			\end{alignat*}
+		\subsection{Double Angle Formulae}
+			\begin{align*}
+				\sin(2\theta) &= 2\sin\theta\cos\theta\\
+				\cos(2\theta) &= \cos^{2}\theta - \sin^{2}\theta\\
+				&= 2\cos^{2}\theta - 1\\
+				&= 1 - 2\sin^{2}\theta
+			\end{align*}
+
+	\ifSubfilesClassLoaded{%
+		\vbox{\rulechapterend}}{\vspace*{\parskip}\rulebookend}
+
+\end{document}