Proper way to specify an angle

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This is less a math question and more a semantic one. Suppose A and B are two arbitrary axes and I'm interested in an angle of a vector emanating from the origin. If I refer to vector's "angle between A and B" does this grammatically mean that the A-axis points right, the B-axis points up and the angle is traced counterclockwise from A to B? Thus, if I referred to the vector's "angle between B and A" then the axes would be flipped: B would be what is traditionally the x-axis and A would be the traditional y-axis.

I'm afraid I might be off here...as in this phrase structure could be informal and may have no standard meaning. If that's the case, how should I distinguish between these two angles? (I'm assuming the axis names are fixed and can't just be relabeled however is most convenient.)

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By convention, an angle is always measured as increasing in a counter-clockwise manner, and decreasing in a clockwise manner. For a fractional circular measure which increases clockwise and decreases counter-clockwise, the correct terminology is a bearing. So if you were to report a fractional circular measure of direction of a vector $\mathbf{v}$ which increases from the $y$-axis in a clockwise manner, you could say, "The vector $\mathbf{v}$ has a bearing of $57.3^\circ $ [to the $y$-axis]," where [to the $y$-axis] can be omitted if there is a convention that is made obvious. I have never seen the term bearing used mathematics, since we can easily give a negative angle. However, it is frequently used in real world navigation, where the convention for the $y$-axis is North.