Added the sin function to an equation and removed a duplicated sentence.

chapters/rigidBody.tex

@@ -58,7 +58,7 @@ \subsection{Points, Vectors, and Coordinate Systems}
 	\end{array}} \right] \mathbf{b} \buildrel \Delta \over = { \mathbf{a}^ \wedge } \mathbf{b}.
 \end{equation}
 
-The result of the outer product is a vector whose direction is perpendicular to the two vectors, and the length is $ \left | \mathbf{a} \right | \left | \mathbf{b} \right | \left \langle { \mathbf {a}, \mathbf {b}} \right \rangle  $, which is also the area of the quadrilateral of the two vectors. From the outer product operations, we introduce the $ ^ \wedge $ operator here, which means writing $ \mathbf{a} $ as a \textit {skew-symmetric matrix} \footnote{Skew-symmetric matrix means $ \mathbf{A} $ satisfies $ \mathbf{A}^T=- \mathbf{A}$. }. You can take $ ^ \wedge $ as a skew-symmetric symbol. It turns the outer product $ \mathbf{a} \times  \mathbf{b} $ into the multiplication of the matrix and the vector $ { \mathbf{a}^ \wedge } \mathbf{b} $, which is a linear operation. This symbol will be used frequently in the following sections. This symbol will be used frequently in the following sections. It is a one-to-one mapping, meaning that for any vector, it corresponds to a unique anti-symmetric matrix, and vice versa:
+The result of the outer product is a vector whose direction is perpendicular to the two vectors, and the length is $ \left | \mathbf{a} \right | \left | \mathbf{b} \right | \left \sin \langle { \mathbf {a}, \mathbf {b}} \right \rangle  $, which is also the area of the quadrilateral of the two vectors. From the outer product operations, we introduce the $ ^ \wedge $ operator here, which means writing $ \mathbf{a} $ as a \textit {skew-symmetric matrix} \footnote{Skew-symmetric matrix means $ \mathbf{A} $ satisfies $ \mathbf{A}^T=- \mathbf{A}$. }. You can take $ ^ \wedge $ as a skew-symmetric symbol. It turns the outer product $ \mathbf{a} \times  \mathbf{b} $ into the multiplication of the matrix and the vector $ { \mathbf{a}^ \wedge } \mathbf{b} $, which is a linear operation. This symbol will be used frequently in the following sections. It is a one-to-one mapping, meaning that for any vector, it corresponds to a unique anti-symmetric matrix, and vice versa:
 
 \begin{equation}
 \mathbf{a}^\wedge = \left[ {\begin{array}{*{20}{c}}