Putting an exponent on a function symbol like that usually means either a typical exponential/power, except when it’s -1, in which case it’s a functional inverse. sin^(-1)(x) is the functional inverse of sin(x), which is not the same as the reciprocal (sin(x))^(-1). Some people even use sin^(a)(x) where a is an integer to denote functional composition, so sin^(2)(x) = sin(sin(x)).
What’s wrong with sin^2(x)?
Putting an exponent on a function symbol like that usually means either a typical exponential/power, except when it’s -1, in which case it’s a functional inverse. sin^(-1)(x) is the functional inverse of sin(x), which is not the same as the reciprocal (sin(x))^(-1). Some people even use sin^(a)(x) where a is an integer to denote functional composition, so sin^(2)(x) = sin(sin(x)).
Besides that pretty major issue, nothing.