if you sine something and then arcsine it, you get the original thing again.

arcsin(sin x) = x if pi/2 =< x < pi

arcsin(sin x) = 0 if x = pi

i have two answers above, why? we have to account for the fact that our calculators always takes us back to the reference angle, which is not always the same as the original angle.

so in general, for this problem, we should say something like:

for some integer

and we choose the appropriate k