Talk:Cosine error

"Citation Needed" Rampage
Why are so many self-evident explanations marked as 'citation needed', and a massive warning plonked at the top of the page? I can't see any particular issues with the introduction to this article, and I've been editing WP for well over ten years. When I see this kind of thing I usually smell a pedant on the prowl! Blitterbug 08:32, 21 May 2022 (UTC)

Definition and rectangle example
Unfortunately the article doesn't properly define what cosine error is. I would expect it to be the error that occurs when you're supposed to be measuring a vector quantity parallel to the vector (say a magnetic field) to get its magnitude $$a$$ but are actually measuring at a small angle $$\theta$$ to it. So instead of $$a$$ you get $$a\cos \theta$$, and the error is $$a(1-\cos \theta)$$.

An everyday example of that would be weighing something on a kitchen scale which isn't quite level. The weight is a force acting vertically downwards, but you're not measuring vertically and therefore get a not-quite-vertical component of the weight instead of the true value.

The rectangle example seems to me to have two problems: Musiconeologist (talk) 15:04, 30 March 2024 (UTC)
 * The measured distance will be $$\frac{a}{\cos \theta}$$, not $$a\cos \theta$$. Even if this falls under the definition, it's more complicated for a reader than necessary.
 * Width isn't a vector quantity, and we've said the error happens with vectors.


 * OK, I've just had a look at the Dover Motion reference and the meaning it gives is exactly the same as my guess, right down to the formula. some of the references, and it seems to be used both ways round, for situations where a measurement has to be either multiplied or divided by the cosine of an error angle. If that can be clarified, I'll do some rewriting and hopefully the article will no longer need cn templates sprinkled all over it.
 * What's needed in my opinion isn't more citations, but one citation containing a good, clear definition, and a clear explanation in the article of its meaning. Any maths involved in that will be routine calculation, since it needn't be any more complicated than what I've said above; and it can be verified by doing the calculation oneself. Musiconeologist (talk), edited 18:37, 30 March 2024 (UTC)

Intro now rewritten
I set out to correct the errors and confusions in the introduction, which ended up completely rewritten. Helpfully, the Dover reference draws attention to the error working the opposite way round for two different instruments, so I was able to mention both.

I think the next section needs two examples: one where the cosine error multiplies the true value by $$\cos\theta$$, and one where it divides by $$\cos\theta$$. Musiconeologist (talk) 02:44, 31 March 2024 (UTC)