The following are the matrices that represent rotations anticlockwise about the $x$, $y$ and $z$ axis respectively: $$\begin{pmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta \\ 0 & \sin\theta & \cos\theta \end{pmatrix}$$
$$\begin{pmatrix} \cos\theta & 0 & \sin\theta \\ 0 & 1 & 0 \\ -\sin\theta & 0 & \cos\theta \end{pmatrix} $$
$$\begin{pmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{pmatrix} $$ My question is, when we say anticlockwise what exactly do we mean?
Do we mean anticlockwise when facing in the positive direction of the given axis or anticlockwise when facing in the negative direction of the given axis?
Thank you very much for your help.
Assuming a “standard” right-handed coordinate system, it means if you stick the thumb of your right hand in the positive direction of the axis, the rotation is in the direction of the curl of your fingers.
Were we using the alternative left-handed system, the rotation would be in the other direction.
Edit: We say that the system is right-handed if, when your right thumb is pointing straight up in the positive z direction, and your right fingers are pointing in the positive x direction, your fingers curl in the direction of positive y. When you use your left hand to determine positive y, you get a left-handed system.