There is no semantic for the rotation matrix alone... you have the World matrix, which is a combination of translation, rotation and scaling. (see
this page for all supported semantics in TV3D)
BUT, if your mesh isn't scaled, you can extract the rotation matrix from the world matrix.
By casting the world matrix to a 3x3, you get the combination of rotation and scaling. If scaling is an identity, you get rotation.
Then the sinusoidal offset would be a push in the X or Z direction, but transformed by this rotation matrix, which makes it relative to its current orientation.