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News from Mathnasium of Round Rock

secret trig functions!

Oct 27, 2017

 

On Monday, the Onion reported that the "Nation's math teachers introduce 27 new trig functions." It's a funny read. The gamsin, negtan, and cosvnx from the Onion article are fictional, but the piece has a kernel of truth: there are 10 secret trig functions you've never heard of, and they have delightful names like "haversine" and "exsecant."

A diagram with a unit circle and more trig functions than you can shake a stick at. (It's well known that you can shake a stick at a maximum of 8 trig functions.) The familiar sine, cosine, and tangent are in red, blue, and, well, tan, respectively. The versine is in green next to the cosine, and the exsecant is in pink to the right of the versine. Excosecant and coversine are also in the image. Not pictured: vercosine, covercosine, and haver-anything. Image: Limaner and Steven G. Johnson, via Wikimedia Commons.

Whether you want to torture students with them or drop them into conversation to make yourself sound erudite and/or insufferable, here are the definitions of all the "lost trig functions" I found in my exhaustive research of original historical texts Wikipedia told me about.

Versine: versin(θ)=1-cos(θ)
Vercosine: vercosin(θ)=1+cos(θ)
Coversine: coversin(θ)=1-sin(θ)
Covercosine: covercosine(θ)=1+sin(θ)
Haversine: haversin(θ)=versin(θ)/2
Havercosine: havercosin(θ)=vercosin(θ)/2
Hacoversine: hacoversin(θ)=coversin(θ)/2
Hacovercosine: hacovercosin(θ)=covercosin(θ)/2
Exsecant: exsec(θ)=sec(θ)-1
Excosecant: excsc(θ)=csc(θ)-1

Ref : https://blogs.scientificamerican.com/roots-of-unity/10-secret-trig-functions-your-math-teachers-never-taught-you/