Are trigonometry functions Ratios or Distance? Consider a point, say $S(2,3)$. Now here $3$ indicate that $S$ is $3$ units away from x axis. Right? 
Now consider what Wikipedia says: 

The trigonometric functions cos and sin are defined, respectively, as
  the x- and y-coordinate values of point A.

This definition of $sin$ and $cos$ is based on unit circle. In this definition sin is defined as Y-coordinate of point $A$ on unit circle. But now what do we mean by Y-coordinate? 
Y-coordinate is distance between point $A$ to $x$-axis (Right? ).
How could sin or for that matter any trigonometric function can be a distance? Trigonometry functions, for acute angle, are defined as ratios of sides. How could they be "distance"(with unit) in one definition and "ratio" (unitless) in other?

Given a circle centered at the origin with radius $R$ we define the the $x$ and $y$ coordinate values of point $A$ as


*

*$x=R\cos \theta \implies \cos \theta=\frac x R$

*$y=R\sin \theta\implies \sin \theta=\frac y R$
therefore both $\cos \theta$ and  $\sin \theta$ are ratio, that is dimensionless values, even if in the definition we refer to a unit circle ($R=1$).
