Recall that for all x,
cos²(x) + sin²(x) = 1
So we have
sin(x) = ± √(1 - (60/61)²) = ± 11/61
Recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
From here, we get
sin(2x) = 2 (± 11/61) (60/61) = ± 1320/3721
In case you meant to ask about sin²(x), we get
sin²(x) = 1 - cos²(x) = 121/3721
