Question

rewrite using radicals and rational numbers

Cos 3(pi)/8

Answer 1

Let a = 3 pi/4 = 135 degrees

cos a = -(sqrt 2)/2
You want cos (a/2)= cos (3 pi/8)
Use the identity:
cos (a/2) = sqrt[(1/2)(1 + cos a)]
= sqrt[(1/2)(1 - (sqrt2/2)]
= sqrt[(1/2) -(sqrt2)/4]