K-Form (Precalc/Calculus)?

The directions say "Solve 0<x<2(pi) in k-form & give the values of k. I have no idea what k-form is and/or where k comes into the situation. My teacher only gave one little example as an explanation and I can't make heads or tails of it: sin2x=1/2 2x=pi/6 + 2k(pi) 2x=(5pi)/6 + 6k k= 0,1 x= pi/12 +... show more The directions say "Solve 0<x<2(pi) in k-form & give the values of k.
I have no idea what k-form is and/or where k comes into the situation.
My teacher only gave one little example as an explanation and I can't make heads or tails of it:
sin2x=1/2
2x=pi/6 + 2k(pi)
2x=(5pi)/6 + 6k

k= 0,1
x= pi/12 + k(pi)
x=(5pi)/12 + k(pi)
x= pi=12, 13(pi)/12, 5(pi)/12, 17(pi)/12

Any help would be appreciated BEYOND BELIEF.
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