Hi Forum

Using intervals and inequalities can get a little tricky, so here is my question.

Find all of the degree-measure of all the angles x in the interval $\displaystyle 0º\leq x \leq 360º$ for which

$\displaystyle 2(sin{x}+cos{x})<\sqrt{1+2sin{x}cos{x}}$

$\displaystyle 4(sin{2x}+1)<1+sin{2x}$

$\displaystyle sin{2x}<\frac{-3}{3}$

$\displaystyle sin{2x}+1\color{blue}{\geq} 0$

How could this happen?

I know that the sign of the inequality change when dealing with negative numbers or reciprocals, but...

This actually becomes greater then or equal. Can someone explain?

Thanks!