[spec] typo in segment area formula
[notes.git] / spec / spec-collated.tex
index 225cc8c01920230b2558af383d7d7304c9612027..989f7707f20cb52a2481797b2c25d6b66c004b41 100644 (file)
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-                  \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*}