How to rotate bone with different pivot point

How can I rotate a bone by pivoting on the tip rather than root? An illustration of my question:

1: A basic rig
2: If I rotate bone A, I get this.
3: If I rotate bone B (from the position in 1) , I get this.
4: But I want to force it to do this.

Any suggestions? Is this too vague?

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in the general case, you can use a proxy bone and a copy rotation (local) constraint.

for this case, you can just reverse the orientation of B, extrude it from the base of A in the other direction.

EDIT: whoops, nevermind. Totally misunderstood what you were trying to do. Ignore me. :stuck_out_tongue: