[the_origami_fox]

Yes you're right. It has to do with how he derived the approximation formula for the natural logarithm. He needed a function y=sin(x) for his log(y) calculations. But I am not sure when the log(f(x))) tables for the other trigonometric functions came about. As far I understood, initially a single log(y) table sufficed.

[_4gzn]

Well, I suppose Napier presaged the concept of a single source of truth. Aren't other log-trig tables a waste of paper if you can look up log(cos x) under log(sin(90°−x)) and quickly calculate log(tan x) as log(sin x)−log(cos x)?