Question

How do you solve: `sin(sin^-1 (0.9))`?

Answer 1

I'm going to assume that by `sin^(-1)` what is intended is what is also called the `arcsin` (the inverse of the `sin` function) and not the value of the `sin` function to the exponent of `-1`.

If this is the case, then by definition
`sin(arcsin(0.9)) = 0.9`

If you intended the `(-1)` to be an exponent then I know of no way to solve this other than to look-up the (approximated) values using a table of `sin` values or a calculator.