How to solve this question? Help please..

A sin function (f(x)=sin(x)) is a wave that starts at f(x)=0 @ x=0, increasing to f(x)=1 @ x=π/2, then f(x)=0 at x=π, f(x)=-1 @ x= 3π/2, and returning to 0 @ 2π.

So if sin(8x)=0.92 then (8x)-sin^(-1)(0.92). A simple calculator gives that (8X)=0.3718π ,but there is a second solution that is the one just past x=π/2, when f(x) is decreasing, but still positive at π/2+(π/2-0.3718 π)=(1-.3718)π.

So for solution of x, there are two x=[0.3718π]/8 and x=[(1-.3718)π]/8

If you plot a sin wave over a full cycle (2π), you'll see where both solutions come from (remember to divide by the constant)

Rap

Agreed, but there are more solutions than that. Since x can vary from 0 to 2pi, 8x will go from 0 to 16pi. There will be two solutions in each cycle and eight cycles, so 16 solutions overall.