I have the yaw and pitch of my unit at my disposal, I know if I use polar to cartesian conversion I'll get the X and Y of each one of those two, but I need them combined to give me the x,y and z of the direction I'm facing.
If you're using a regular Unity GameObject, you can just use
transform.forward to access the forward direction of your object. See the Unity documentation for details.
If you're using a different way to track your object, Spherical coordinates are essentially polar coordinates expanded with a third dimension.
EDIT: I assume in Minecraft
z is the vertical axis and
y are on the horizontal plane. If this isn't the case, the principles would still apply but the
z would need to be assigned differently:
y directional components can be determined from the yaw fairly easily:
x = sin(yaw) and
y = cos(yaw). I'm not familiar with modding Minecraft to know whether or yaw is in degrees or radians—you may need to convert it in order to get real results from those trig functions. It's also possible that you may need to add a constant to the yaw to match the actual axes in the game (like adding or subtracting 90° to align with the world axes).
z component can be determined from the pitch:
z = cos(pitch). Again, you may need to convert between degrees and radians or add a constant to match world axes.
If you have the Yaw and Pitch giving you the X and Y, can't you just assuming your roll (Z) is 0? Most game characters don't allow you to rotate on that axis.