Comments on: How many trig functions are there?

By: John Armstrong

John Armstrong — Fri, 05 Feb 2010 19:52:19 +0000

2) Sine and Cosine may be related as you indicate, but they’re a very important pair. Specifically, they provide an orthogonal basis for the space of solutions to the differential equation

$latex \displaystyle\frac{d^2}{dt^2}u(t)+u(t)=0$

By: Wing

Wing — Tue, 29 Sep 2009 01:19:31 +0000

Thanks for the article. I just read the Wikipedia articles on versine, haversine, etc. and it’s pretty awesome. It’s sad that there’s really no way to actually learn spherical trig anymore in school.

As to why a calc text claims that there are 6 trig functions: a lot of formulas can be expressed more nicely with sec, cos and cot. The derivative of tan is for example secant squared. Also, the 1 + tan^2 =sec^2 identity plays a crucial role in some integrals.

I guess you have as many trig functions as you need. In most cases, it would probably be 0.

By: Sue VanHattum

Sue VanHattum — Sat, 26 Sep 2009 23:15:06 +0000

Thank you! One of the texts I’ve used said something about the most common 6 trig functions, and I was bewildered. I had never gotten around to researching this, so I’m delighted to have it drop into my lap today. Now I know. 6 more antiques to think on, if you wish.

By: tom

tom — Sat, 26 Sep 2009 02:50:56 +0000

I can see the argument for there being no trig functions – and revert back to e and i, but of course these are only elements in a field, not functions in of themselves. The ‘fundamental’ function relating e, i, and sines and cosines is of course the exponential function. For this matter, we can actually just return to sums and products and toss in the weird operation of ‘infinite’ sums of products; or perhaps the ‘limit’ of an infinite sequence of partial sums is even more basic.

By: Mark Durst

Mark Durst — Fri, 25 Sep 2009 21:48:27 +0000

Am now trying to think whether the co- in cosine can be expressed as a special case of the co- in everything else (cohomology, cobordism, etc.)

I’m told that at Mathcamp last year, two individuals agreed to share the job of coordinator. So they were, of course, called the ordinators.

By: josh reich

josh reich — Fri, 25 Sep 2009 19:07:24 +0000

There are no trig functions, only e and i.