Abstract Geometry? Are there similar terms in other areas for the idea the "angle" conveys in geometry ? I find that functions for abstract things such as pressure,electrical currents ( nothing geometric there ) on AC circuits are described by the sin function ( argument is an angle, there fore an geometric entity ) .Do we really have that abstract things are necessarily described by geometric entities ?   I understand that we can relate time to angle with the concept of angular frequency, but it seems too unintuitive and unnecessary to have to relate a sin-like variation generally ( a variation that decelerates smoothly towards the peaks and accelerates smoothly towards the center ) with geometry and angles.   
Maybe the concept of angle we know is a simply an example of a greater idea ( like a  a measure of difference between instances of the same thing ) applied to geometry or am i tripping ?
 A: You tagged this question as differential equations, and that gives part of the answer. Many physical objects behave like little springs near equilibrium (like a pendulum almost at rest, a man falling through a hole to the center of the earth, a wobbly top, etc.). One term for this is the harmonic oscillator. Such things can often be described by second order linear differential equations, whose solutions are either polynomial, exponential, involve sin and cos, or a mix of the three.
The not way that the solutions get oscillation, then, is if sin or cos are involved. Thus, sin and cos are, to a very good approximation, the most common kind of wave-like variation in the universe.
A: These things are all cycles with a certain sort of simple behaviour. If you're looking for a picture then angles and circles are a very good way to go, since they also have this behaviour, but that doesn't mean there's actually a physical angle lurking there somewhere. It's less
$$\text{Angles}\rightarrow \text{Cycles}\rightarrow \text{Currents}$$
and more
$$\text{Cycles}$$
$$\downarrow\ \ \ \ \ \ \ \ \ \ \downarrow$$
$$\text{Angles}\ \ \ \  \text{Currents}$$
Sinusoidal waves describe a particularly simple sort of cycle, and so they show up in physical angles. But they also show up in other places where simple cycles occur.
So you are correct in saying that it is unintuitive to relate sine and cosine to geometry and angles all the time, because plenty of times the geometry isn't there. In many cases angles aren't the things that are actually doing the cycling. But the sinusoidal functions still describe cycling behaviour regardless, so they show up in plenty of cases where physical angles are totally irrelevant.
