Below is a sin graph between and .

The horizontal blue line indicates y=0.5.

The vertical blue lines show where this cuts the x-axis.

What you want is every point on the x-axis that is outside the two blue boxes since you can see that if x takes any value inside either of the blue boxes, the corresponding y-value is greater than 0.5.

Now note that when and again when . This is the boundary of the box on the positive x-axis and tells us that x cant take any values between and

Since sin(x) is periodic, if we subtract from the above results we get the values on the negative x-axis that x cant take.

So putting it all together you get that x can take any value in the following range...

, ,