I read in my math book about rotation matrices.

I read about how you derive the formula for making a matrix to rotate about an arbitary axis.

I understood how they made it, and understood the concept of how to do it.

What I don't quite understand, is how to derive the matrices for the "normal" x, y and z axis.

For example, to rotate about the x-axis, the rotation matrix are:

The book didnt say how they derived thease matrices.Code:| 1 0 0 | | 0 cos(x) -sin(x) | | 0 sin(x) cos(x) |

Of course, to derive them, you could just use the arbitary formula with the basis-vectors.

And that's my question. How did they derive the rotation-matrices for the x, y and z axis?

Is it so simple that they figured it out in their head? Can they see it visually/geometricaly?

Or did they derive the formulas using the arbitary formula?