Position not correct when rotate

Hi,
I am a new developer to CNC field and want to perform some drills at some specified positions and directions. Problem is as:

I have a 3Axis machine with an optional rotary axis. I have to drill in the object at some interrelated distances and each drill has to be in some specific direction and each drill may be in different directions. To obtain a direction i use A Axis and them move to specific position and drill. but when i rotate the object, drills are at different position than the required. Also i use to Arc Cosine of Z portion of direction vector to obtain A value.
Now i want to know whether calculation of A (i.e. Arc Cosine of Z-component) is correct or not and if it is wrong, then how should i calculate it. Also guided me about calculation of new position after rotation.

Regards,
Kashif Bashir Bhatti
Software Engineer