Question 969776
Cos (sqrt (2)/2) is at 45 degrees, or pi/4 radians.  That, however is positive.  It becomes negative in the second and third quadrants.  Each of those is pi/2  more.

pi/4+ pi/2= 3 pi/4   That is one solution.
3pi/4+pi/2=5 pi/4  That is the other solution.

In degrees, it is 135 and 225.

{{{graph (300,200,0,6.28,-1.5,1.5,cos(x))}}}