Matrices of Rotation of Axes
Category : JEE Main & Advanced
We know that if \[x\] and \[y\] axis are rotated through an angle \[\theta \] about the origin the new coordinates are given by
\[x=X\,\cos \theta -Y\sin \theta \] and \[y=X\sin \theta +Y\cos \theta \]
\[\Rightarrow \left[ \begin{matrix} x \\ y \\ \end{matrix} \right]=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\,\left[ \begin{matrix} X \\ Y \\ \end{matrix} \right]\Rightarrow \left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\]
is the matrix of rotation through an angle \[\theta \].
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