Why are the Trig functions defined by the counterclockwise path of a circle? My understanding is that $\cos$ is defined by the value of $x$ as you trace the graph of a circle counterclockwise, starting at the point $(1, 0)$. Similarly, $\sin$ traces the $y$ value. I understand HOW the trigonometric functions work. The issue that has been gnawing at me for years is WHY they are defined that way. There's probably a totally reasonable explanation, I know the history of Trig goes back thousands of years, but I don't understand the reasoning behind defining the Trig functions with the most arbitrary, least intuitive possible rules.
If I had been the person to invent $\cos$ and $\sin$, I would have defined them by starting at the topmost point of a circle, and trace it clockwise. Is that not the most intuitive method? Maybe it's just a modern preference, but it seems to me that we humans like to read things left-to-right, and yet the trig functions are defined starting from a circle's right-most point. Furthermore, $\cos$ and $\sin$ start at $x = 1$ on a circle's graph. Why not start at $x = 0$?
I think this is why so many people have no intuitive understanding of $\sin$ and $\cos$, and why many students get through high school and college by simple rote memorization of what a handful of $x$ values evaluate to in $\sin$ or $\cos$.

One of the above answers is correct but the explanation is incomplete.  The answer has to do with the right-hand rule.  This comes into play when working in three dimensions (calculus 3 especially.)  When we use a three dimensional coordinate system, lay your right hand on the x-axis with the fingers pointing in the positive x direction and the palm facing in the positive y direction.  If you were to close your fingers toward the y-axis, then your thumb would point in the positive z direction.  This is why we set up the 3 dimensional coordinate system in the orientation that we have.  Positive x to positive y yields positive z, positive y to positive z yields positive x, positive z to positive x yields positive y.  The right hand rule comes into effect in many physics applications, electromagnetism being the foremost one that springs to mind.  And thusly, in order to make this a universal standard practice, we start at positive x and move toward positive y when denoting angles, even in two dimensions so that it can translate easily when we add the third dimension, and be in agreement with actual physical properties that can be observed.
