Technically you are still doing cosine similarity with the dot product in the case of unit vectors. If you look at the formula, the cosine of the angle between vectors is the dot product divided by the product of the lengths of each vector. So in this case the length of each vector is 1, so your denominator is 1. So all you have in the numerator is the dot product. So the cosine of the angle is the dot product!

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More discussion and testing here:

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