I am currently prepping for uni having been a few years out of the studying loop (programming as it happens). Anyway, I've been re-reading my A-level notes/exercises and looking through OpenCourseWare stuff and I noticed this assertation in my notes:
Given $a \cos\theta \pm b \sin\theta = c$ then:
$a \sin\theta \pm b\cos\theta = r\sin(\theta\pm\alpha)+c$
$a \cos\theta \pm b\sin\theta = r\cos(\theta\pm\alpha)+c$
Given $r \in \mathbb{N}$, $0 \leq \theta < 2\pi$.
Now, I've heard of fourier series which have a very similar form to these equestions.
So, my question is, is there a relation between the two?
Please bear in mind I know I'm stepping off a cliff and into "unknown unknowns" territory if they are - I have absolutely no idea what harmonic analysis is and I don't (yet) understand fourier series fully, although I grasp roughly how they work. I'm just interested to know if they are related and of course any further information / direction / reading I should follow up. I ask because this was one of those "odd topics" at A-level that we derived in class from a geometric argument then I've never seen again.
Thanks.