Question 37779
The half angle formula for sin(theta) is
sin(theta/2) = ± sqrt[(1 - cos(theta)) / 2]
If we know cos(7pi/4) = sqrt(2) / 2, we just plug it in, so we get 
sin(7pi/8) = ± sqrt[(1 - sqrt(2)/2) / 2]
(It is clumsy to do trig this way, ya know...)