The question:

Find the domain of:

$\displaystyle \sqrt{1 - 2sinx}$

My attempt:

$\displaystyle 1 - 2sinx = 0$

$\displaystyle -2sinx = -1$

$\displaystyle 2sinx = 1$

$\displaystyle sinx = \frac{1}{2}$

I worked out that x = 30 degrees, or Pi/6

So I want the values where sinx is larger than or equal to 1/2:

$\displaystyle \frac{\pi}{6} + 2\pi k <= x <= \frac{5\pi}{6} + 2\pi k$

Where k is an integer.

I thought this made sense, but the answer in my book is:

$\displaystyle -\frac{7\pi}{6} + 2\pi k <= x <= \frac{\pi}{6} + 2\pi k$

What am I doing wrong? :/