Explain the difference between sin^-1(x) and 1/sin(x), Are there different expressions for both these functions?

Question

I am kind of confused 

Answer 1

In sin^-1x, the "-1" is NOT an exponent. It represents the inverse of the sine function. Recall f(x) and f^-1(x).

sin^-1x means the same as arcsin x, i.e., the arc whose sine is x.

 

sin π/6 = 1/2

sin^-1 1/2 = π/6, or arcsin 1/2 = π/2