Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
iirc, haversine is useful for transforming 2-d "as the crow flies" coords to their 3-d equivalents. at longer distances a body's curvature is really noticeable and often overlooked
Interesting. versine has a lovely and intuitive geometric definition. If you construct a right triangle from the origin to some point on the circle, most people who have done trig will know that the x-coordinate of that point is r cos theta, where theta is the angle and r is the radius. Geometrically the distance from the origin to where the triangle rests on the x axis is r cos theta. But what about the rest of that radius? ie the line segment on the x-axis from there to where the circle intersects the x-axis?
That is r versin theta (ie r - r cos theta). Pretty cool no? I mean I've literally never had to find the length of that line, but that's how you would if you wanted to..
It's a US thing. Europeans just write 1/cos(x) instead of treating it as a special thing with its own name. The Americans have sec, csc, and a bunch of others I never bothered to learn. It doesn't seem to add all that much to me? (Of course, it's a bit hypocritical since I gladly use tan(x).)
... which were not used in my education but whenever i saw them i wished they had been, they lay out a geometric interpretation of all of them. by "old" i mean "look like Leonardo drew them"
I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
I know what you mean, but as a sibling pointed out for everyone else's benefit, parent is using the word inverse where they mean reciprocal.
The inverse of cosine is arccosine (sometimes written acos or cos^{-1}). Secant is the reciprocal of cos ie sec x = 1/cos(x)).
Likewise cotan is the reciprocal of tan (1/tan). The inverse of tan is atan/arctan/tan^{-1}.
This is confusing for a lot of people because if you write x^{-1} that means 1/x. If you write f^{-1} and f is a function, then _generally_ it means the inverse of f. In the case of trig functions this is doubly confusing because people write sin^2 theta meaning (sin theta)^2 but sin^-1 theta means arcsin theta.
That's why in my maths studies they started by teaching you to do the inverse with a -1 so when you see it you don't get confused but changed to preferring arcsin etc as this is unambiguous and if you learn to write this way you won't confuse others.
It does not help that both reciprocal and inverse come from French, and that their common meanings are reversed in English. I'm not sure whether the meaning of both words has remained constant over time in these two languages, as they both roughly mean "the opposite" and if you want to avoid ambiguity, you simply add context. For example, if you say "inverse function" or "multiplicative inverse" it's not ambiguous.
That’s right, it’s a distribution. And that fact has me, a non-mathematician, personally caused some huge headaches, because I thought I could treat it just like a function… Yeah, turns out really weird things happen if you try to do so without knowing what you’re doing. For example, taking its square does not make sense.
Oops, replied to the wrong comment. This is the one I meant to reply to, which is talking about the impulse train, which is not a function: https://news.ycombinator.com/item?id=43741539
>Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function
I think we used it in geometry in US high school, but only to complete an assignment or two to show we could use trig functions correctly. I had to relearn how all of them worked to help my kid with homework, it's mostly look at the angles and sides you have available and pick which trig function is necessary to figure out which one you're solving for. I'm sure there are real life uses for trig functions, and I hate to be one of those "when are we ever going to use this" types, but I've never used any of them outside of math classes.
