First look at arccos(4/x).  That asks the question:

"What angle has 4/x for its cosine?"

So we draw a right triangle and let the angle be

arccos(4/x)

and since the cosine is the adjacent over the hypotenuse,

we let the adjacent side be 4 and the hypotenuse be x:

Let the opposite side be h.




All we need now is to find the opposite side h by the 
Pythagorean theorem:







So the triangle is now:



So now the sine of arccos(4/x) is found by taking
the opposite side over the hypotenuse:

sin(arccos()) = 

Edwin