What is the purpose, if any, of secant, cosecant, and cotangent? I’m an engineering student so I use sine, cosine, and tangent a lot, but almost never the other 3. Creating a new trig function just to be the reciprocal seems to be a bit redundant.
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In the days before calculators, they had massive long lookup tables for these kinds of functions. Having extras for the reciprocals made sense, because finding the reciprocal of a rounded decimal is tedious and inaccurate, especially with the risk of human error in there.
These days, they’re basically historical oddities that are rarely used except when they make notation simpler (which I presume is also the reason they got individual names in the first place).
Basically, it wasn’t redundant when the alternative was long division by hand.
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