Question

If cosx=(1/2 + (2^1/2)/2)^1/2 and sinx=-(1/2 - (2^1/2)/2)^1/2 0<x<2pi. It follows that 2x=kpi. The value of k is:

Answer 1

sorry i made a mistake..... Correction cosx=(1/2 + (2^1/2)/4)^1/2 and sinx=(1/2 + (2^1/2)/4)^1/2

Answer 2

since cosx = √(1 + 1/√2)/2) cos2x = 1/√2, so 2x = π/4 or 7π/4

since cosx>0 and sinx<0 only in QIV,
3π/2 < x < 2π
that means 3π < 2x < 4π

Looks like k = 7/4

Answer 3

k = 4