\usepackage{pgfplots}
\usepackage{pst-plot}
\usepackage{rotating}
+%\usepackage{showframe} % debugging only
\usepackage{subfiles}
\usepackage{tabularx}
\usepackage{tcolorbox}
\end{scope}
\end{tikzpicture}
- \subsubsection*{Sectors}
\begin{align*}
- A &= \pi r^2 \dfrac{\theta}{2\pi} \\
+ \textbf{Sectors: } A &= \pi r^2 \dfrac{\theta}{2\pi} \\
&= \dfrac{r^2 \theta}{2}
\end{align*}
- \subsubsection*{Segments}
-
- \[ A = \dfrac{r^2}{2} \left( \theta = \sin \theta \right) \]
-
- \subsubsection*{Chords}
+ \[ \textbf{Segments: } A = \dfrac{r^2}{2} \left(\theta - \sin \theta \right) \]
\begin{align*}
- \operatorname{crd} \theta &= \sqrt{(1 - \cos\theta)^2 + \sin^2 \theta} \\
+ \textbf{Chords: } \operatorname{crd} \theta &= \sqrt{(1 - \cos\theta)^2 + \sin^2 \theta} \\
&= \sqrt{2 - 2\cos\theta} \\
&= 2 \sin \left(\dfrac{\theta}{2}\right)
\end{align*}