Simulator Mechanics

Hey hey,

I am trying to make a flight simulator.
But having a problem with rotations.

I know the distance travalled and know the angle of the x and z axis.

In 2D rotation is simple :
zi = Math.sin(Math.toradians( z-rotation) )
xi = Math.cos(Math.toradians(z-rotation))

in 3D you also have the y-axis movement.
I can make it wordk, that the rotation is showing, that the object moves along the X and Y axis, but it also is moving over the Z-axis.

How do you calculate the complete movement over the axis of the object. ?? ??? ???