Posted by Jon on Sunday, December 5, 2010 at 5:55pm.
Make a triangle.
By Pythagoras
r^2 = 5^2 + 12^2
r = 13
so sinx = 5/13 and cosx = 12/13
I will assume you meant sin(x/2)
using cosx = 1 - 2sin^2 (x/2)
12/13 = 1-2sin^2 (x/2)
2sin^2 (x/2) = 1/13
sin^2 (x/2) = 1/26
sin (x/2) = 1/√26 or √26/26