Pre-calculus/trig

2sin^2 x = 1       divide both sides by 2

sin^2 x  =  1/2      take both roots

sin x = 1 /√2        or   sin x = -1 / √2

sin x = 1/√2   at   pi/4  and 3pi/4      on   [0, 2pi ]

sinx = -1 / √2  at  5pi/4 and 7pi/4    on [ 0, 2pi ]

So.....it appears that this happens  every 90°   after pi/4  or....expressed another way....at

pi/4 +  pi/2 * n      where n is an integer