Sue, yes, apparently they did. I think this method might become efficient if the numbers were several digits long and you had a really good table: looking up numbers would be faster than other kinds of calculations, and apparently some tables gave values not just to the nearest minute, but down to every second of a degree.
(I think there were also some calculations that came up in astronomy where you’d already be dealing with the sine or cosine of angles and you then had to multiply them, so in those specific cases these formulas would be much more natural to use.)

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