# JEE Main & Advanced Mathematics Matrices Matrices of Rotation of Axes

## 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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