QuestionSolve for the general form of all solutions: $2 \cos (x)=1$ Give your answers as radian measures rounded to 4 decimal places. The "pattern" part of your answers should be $k \pi$ or $2 k \pi$. If you do not need both answer boxes, enter DNE instead of leaving one blank. $x=$ $\square$ or $x=$ $\square$ , where $k \in \mathbb{Z}$.

Studdy Solution
Since the cosine function is periodic with a period of $2\pi$, the general solutions can be expressed as:
$$x = \frac{\pi}{3} + 2k\pi$$ $$x = \frac{5\pi}{3} + 2k\pi$$
where $k \in \mathbb{Z}$.
The general form of all solutions is:
$$x = \frac{\pi}{3} + 2k\pi$$ or $$x = \frac{5\pi}{3} + 2k\pi$$
where $k \in \mathbb{Z}$.