Which of these rotation matrices represents a positive rotation in three-space about the y-axis?

Question

This is what Wikipedia says:

\begin{bmatrix} \cos \theta & 0 & \sin \theta \\ 0 & 1 & 0 \\ -\sin \theta & 0 & \cos \theta \\ \end{bmatrix}

This is what I think it should be:

\begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \\ \end{bmatrix}

Which is correct?

The convention used on the Wikipedia page for the other two transformations suggests that they are using a different standard for rotations about the x axis and the z axis than they are for rotations about the y axis.

Answer 1

It's, for all practical purposes, a matter of opinion in this case. It depends on where you are measuring $\theta$ from, and different people have different conventions in $3$-space.