Tangential movement function design

I need to be able to move my Z axis in a rotary direction to maintain
a tangential perspective to my X and Y motion. Like putting a pizza
cutter on my Z axis with a moving table design. I need to move the
cutter in the proper direction (tangent) to the expected motion.

I tried to avoid this complication by using a free floating drag
knife design but I need to be able to reverse direction immediately
and the radius on the drag knife is too large.

I can easily attach a rotary axis to my Z and have the movement
available but I need a general mathematical function for calculating
the required angle. I was thinking a simple differential equation
could output the required tangent but I simply have not been able to
program the function in C to take into account reversal of direction
or undefined tangents. The ones I have problems with would be like:

last position x=0 y=0
current position x = 2 y = 1 current Z angle is 33 degrees
move to x=2 y = 6
or
last position x=0 y=0
current position x = 2 y = 1 current Z angle is 33 degrees
move to x = -2 y = -6.

Does anyone have the function(s)? They don't have to be in C.