Given cosx = 60/61, find sin2x

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