Ask HN: How does choice of coordinate system affect 3D transformation?

I am going through rotation about an arbitrary axis in three dimensions, rotation about x, y and z-axes in three dimensions etc.

And there are coordinate system that are called as:

- left handed coordinate system

- right handed coordinate system

For some reasons I have observed ambiguousness in various rotation matrices.

Example: Rotation about y-axis by t could be written as:

    $$
    \begin{bmatrix}
    cost & 0 & -sint & 0 \\
    0 & 1 & 0 & 0 \\
    sint & 0 & cost & 0 \\
    0 & 0 & 0 & 1
    \end{bmatrix}
    $$
    

I have seen someone interchanging the sin of sint in some textbooks/authors/videos(like this: https://www.youtube.com/watch?v=ZEXpxIwpGbY)

Check 25:28 of the video and step numbered (3).

This is frying my brain since few days. I know getting free assistance in this huge topic is not possible. But even if you could display a small support, small guidance, that would be greatly push me through this phase.

References:

https://stackoverflow.com/questions/19747082/how-does-coordinate-system-handedness-relate-to-rotation-direction-and-vertices