[NOTES/CM-08012] Matrices for Rotations about Coordinate Axes

The matrix \(\underline{\sf R}\) for rotations about different coordinate axes by an angle \(\theta\) are given by
\begin{eqnarray}
\text{Rotation about }X_1 \text{ axis } &\qquad& \begin{pmatrix}1&0&0\\0& \cos\theta & \sin \theta \\0& -\sin\theta & \cos\theta \end{pmatrix}\\[2mm]
\text{Rotation about }X_2 \text{ axis } &\qquad& \begin{pmatrix}\cos\theta &0& -\sin\theta\\0&1&0 \\-\sin\theta &0& \cos\theta \end{pmatrix}\\[2mm]
\text{Rotation about }X_3 \text{ axis } &\qquad& \begin{pmatrix}\cos\theta & \sin \theta &0 \\ -\sin\theta & \cos\theta &0 \\ 0 & 0& 1 \end{pmatrix}
\end{eqnarray}
By convention, the angle of rotation is taken to be positive using right hand rule.