Using the principal arc-cosine, this formula gives a rotation angle satisfying 0 ≤ ≤ α α ≤ ≤ 180 ∘ ∘ . The corresponding rotation axis must be defined to point in a direction that limits the rotation angle to not exceed 180 degrees. (This can always be done because any rotation of more than 180 degrees about an axis m can always be written as a rotation having 0 ≤ ≤ α α ≤ ≤ 180 ∘ ∘ if the axis is replaced with n = − − m .)