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Your math teacher never taught you these because they're just labels attached to quantities expressible in terms of sine and cosine. They don't aid mathematica

Your math teacher never taught you these because they're just labels attached to quantities expressible in terms of sine and cosine. They don't aid mathematical understanding, and they don't let you solve any problem that you couldn't before.

jloughry 13y ago
...they don't let you solve any problem that you couldn't before But they did have a purpose, years ago. Before pocket calculators, when people used slide rules and log tables, a table of haversines helped avoid nasty loss-of-precision errors near the roots of a function.
- dalke 13y ago
  To emphasize your response, the article goes into depth on this exact point: > I must admit I was a bit disappointed when I looked these up. They’re all just simple combinations of dear old sine and cosine. Why did they even get names?! ... > The secret trig functions, like logarithms, made computations easier. Versine and haversine were used the most often. Near the angle θ=0, cos(θ) is very close to 1. If you were doing a computation that had 1-cos(θ) in it, your computation might be ruined if your cosine table didn’t have enough significant figures.
jpmattia 13y ago
> Your math teacher never taught you these because they're just labels attached to quantities expressible in terms of sine and cosine. ... which is why I plan to ignore tangent from now on.
- waqf 13y ago
  And also sec, cosec, cot. But notice they are at least not polynomial in cos and sin, whereas the functions introduced in this article are. To be erudite about it, there are essentially no other trig functions than cos and sin, in the sense that cos and sin (aka x and y) generate the ring of polynomial functions on the circle, ℂ[x,y]/(x²+y²-1). Versine etc. are elements of the ring and therefore they are generated (as polynomials) by cos and sin, whereas tan etc. are not elements of the ring because they sometimes go to infinity (they're elements of the larger function field).
mistercow 13y ago
That would apply to tangent, cotangent, secant, and cosecant as well, and yet you still learn those (even though, at least in my experience, high school trig didn't attempt to give any foundation for what the hell any of those are (other than tangent), besides their relationships to the other functions.
- deleted 13y ago
  [deleted]
- FkZ 13y ago
  I don't know if it's a difference in education systems or the individual teachers, but I didn't learn about any of those other than tangent until I entered university, and then only as a side note in a calculus text book.
saraid216 13y ago
For serious. Why wasn't math class just "Look, here's an empty set. Go forth and do math."? /s
comrade_ogilvy 13y ago
Tan, cotan, sec, cosec have practical value in calculus. It might be a little unfair to expect your trig teacher to prove that to you.
- FkZ 13y ago
  If they're going to be taught, it is fair to expect the motivation for teaching them.
baddox 13y ago
Or conversely, sine and cosine are just labels attached to quantities expressible in terms of coversine, versine, etc.
alexkus 13y ago
Given that:- sin(x) = cos( pi/2 - x ) cos(x) = sin( pi/2 - x ) you only need one of them.

jloughry 13y ago

...they don't let you solve any problem that you couldn't before But they did have a purpose, years ago. Before pocket calculators, when people used slide rules and log tables, a table of haversines helped avoid nasty loss-of-precision errors near the roots of a function.

dalke 13y ago
To emphasize your response, the article goes into depth on this exact point: > I must admit I was a bit disappointed when I looked these up. They’re all just simple combinations of dear old sine and cosine. Why did they even get names?! ... > The secret trig functions, like logarithms, made computations easier. Versine and haversine were used the most often. Near the angle θ=0, cos(θ) is very close to 1. If you were doing a computation that had 1-cos(θ) in it, your computation might be ruined if your cosine table didn’t have enough significant figures.

jpmattia 13y ago

> Your math teacher never taught you these because they're just labels attached to quantities expressible in terms of sine and cosine. ... which is why I plan to ignore tangent from now on.

waqf 13y ago
And also sec, cosec, cot. But notice they are at least not polynomial in cos and sin, whereas the functions introduced in this article are. To be erudite about it, there are essentially no other trig functions than cos and sin, in the sense that cos and sin (aka x and y) generate the ring of polynomial functions on the circle, ℂ[x,y]/(x²+y²-1). Versine etc. are elements of the ring and therefore they are generated (as polynomials) by cos and sin, whereas tan etc. are not elements of the ring because they sometimes go to infinity (they're elements of the larger function field).

mistercow 13y ago

That would apply to tangent, cotangent, secant, and cosecant as well, and yet you still learn those (even though, at least in my experience, high school trig didn't attempt to give any foundation for what the hell any of those are (other than tangent), besides their relationships to the other functions.

deleted 13y ago
[deleted]
FkZ 13y ago
I don't know if it's a difference in education systems or the individual teachers, but I didn't learn about any of those other than tangent until I entered university, and then only as a side note in a calculus text book.

saraid216 13y ago

For serious. Why wasn't math class just "Look, here's an empty set. Go forth and do math."? /s

comrade_ogilvy 13y ago

Tan, cotan, sec, cosec have practical value in calculus. It might be a little unfair to expect your trig teacher to prove that to you.

FkZ 13y ago
If they're going to be taught, it is fair to expect the motivation for teaching them.

baddox 13y ago

Or conversely, sine and cosine are just labels attached to quantities expressible in terms of coversine, versine, etc.

alexkus 13y ago

Given that:- sin(x) = cos( pi/2 - x ) cos(x) = sin( pi/2 - x ) you only need one of them.