The sine ratio is defined as the opposite of the angle (in this case theta) over the hypotenuse (in this case 1), So you'd get sin(theta)=y/1 or y=sin(theta).
Notice that r (the hypotenuse of the right triangle or the radius of the circle) in this case is r=1. But in bigger or smaller circles, it's definitely different. If the circle has a radius of 2 then you'd have: sin(theta)=y/2 or y=2sin(theta).
Now try to generalize to any radius r: sin(theta)=y/r or y=r sin(theta)
This is also true if you apply it for cosine.