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.

Question

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.

In: 20

Answer 1

You don’t *have* to use them explicitly. The functions sec, cosec and cot are just 1/cos, 1/sin and 1/tan respectively, and indeed some prefer to just use the latter. But they’re traditional names for completeness’s sake and the old trig and differentiation/integration formulas are usually still written with them, so people still use them.

It’s like ‘What’s the point of this obscure word that has a synonym, this random irregular verb or quirk of English spelling?’ You could come up with a more streamlined version of the language without, but you’ll need to understand them when others use them.