Mathematics

The key is recognizing that $\cos 2x = \frac{1}{2}$ asks: "at what angles is cosine equal to $\frac{1}{2}$?" You know cosine hits $\frac{1}{2}$ at $60°$ and $300°$ (or $\frac{\pi}{3}$ and $\frac{5\pi}{3}$ in radians) within one cycle. Since cosine repeats every $360°$, you need to account for all those angles plus the periodicity—and remember that your variable is $2x$, not $x$, so you'll need to solve for $x$ at the end.

The key is recognizing that $\cos 2x = \frac{1}{2}$ asks: "at what angles is cosine equal to $\frac{1}{2}$?" You know cosine hits $\frac{1}{2}$ at $60°$ and $300°$ (or $\frac{\pi}{3}$ and $\frac{5\pi}{3}$ in radians) within one cycle. Since cosine repeats every $360°$, you need to account for all those angles plus the periodicity—and remember that your variable is $2x$, not $x$, so you'll need to solve for $x$ at the end.