What is the trigonmetric fact for sin 3.14/8?

Answer 1

I recognize your 3.14, most probably meant to stand for π
so you want sin π/8 or sin 22.5°

recall that cos 2A = 1 - 2sin^2 A
then cos 45° = 1 - 2sin^2 2.5°
2sin^2 22.5° = 1 - cos45° = 1 - √2/2
= (2 - √2)/2

sin^2 22.5 = (2 - √2)/4

sin 22.5 = sin π/8= √(2 - √2) / 2