It depends on your context, and is mentioned in the article. The advantage of turns comes from the fact that the implementation of sinᵣ etc. is internally doing

It depends on your context, and is mentioned in the article. The advantage of turns comes from the fact that the implementation of sinᵣ etc. is internally doing a conversion to turns, so by using sin_turns directly, you avoid calculating π/π with every call. It’s not a call for someone doing calculus or solving differential equations to abandon radians, just for the particular case of getting a numerical value for sin, cos, etc. from a library, having direct access to a turns-based function would produce faster code and also avoid some of the rounding errors that come from that π/π not to mention the imprecision of any angle that isn’t 0.