# Trig reciprocal function nomenclature?

The fact that the reciprocal of $\sin\theta$ is $\csc\theta$, and the reciprocal of $\cos\theta$ is $\sec\theta$ messed with my head for the longest time when I was taking trig. Why are the functions named this way, when an alliterative scheme would seemingly be more sensible?

While I'm at it, what's the reason for choosing the names sine, cosine, and tangent? The words sinusoidal and tangental come to mind, but perhaps these words could have come from the function names, not the other way around.

• The properties of secant align better with the properties of sine than the properties of the cosine. For example, if you look at the formulas for the derivatives, the derivatives of sine, tangent, and secant have no minus sign, while the derivatives of cosine, cotangent, and cosecant all have a minus sign in them. – Arturo Magidin Nov 28 '11 at 3:27
• For the etymology, you can see Wikipedia. "Sinusoidal" is derived from "sine"; sine is derived from the Sanskrit word for "chord" (via Arabic), since sines were originally related to lengths of certain chords in circles. Tangent comes from the Latin for "touching", and it is also related to circles (and tangent lines to the circles). – Arturo Magidin Nov 28 '11 at 3:30
• Throw in versine, vercosine, haversine, coversine, hacovercosine, and excosecant, and you get a party... – Srivatsan Nov 28 '11 at 3:55