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generally, ^(-1) of a function implies the inverse of the function. For example if f(x) = 2(x^2) then f^-1(x) = (1/2x)^0.5. not simply 1/f(x)

You need to recognise the other solutions, x=pi/12...

I wasn't dividing by sin, i was using the inverse sin operator on both sides, where sin^{-1}(sin(x)) = x. This is perfectly acceptable, and all scientific calculators have this function.

Also, the...

simple algebra:

sin(2x) = \frac{1}{2}

2x = sin^{-1}(\frac{1}{2})

x = \frac{sin^{-1}(\frac{1}{2})}{2}

This will give you the lowest value of x. You need to remember that there are in fact...