## Algebra and Trigonometry 10th Edition

$x=\frac{4\pi}{3}$
$2~cos\frac{x}{2}+1=0$ $cos\frac{x}{2}=-\frac{1}{2}$ $\frac{x}{2}=\frac{2\pi}{3}$ or $\frac{x}{2}=\frac{4\pi}{3}$ (with $0\lt\frac{x}{2}\lt2\pi$) If $x$ is in the interval $[0,2\pi)$, then $\frac{x}{2}$ is in the interval $[0,\pi)$ The solution for $x$ is in the interval $[0,2\pi)$: $\frac{x}{2}=\frac{2\pi}{3}$ $x=\frac{4\pi}{3}$