Use the unit circle shown here to solve the trigonometric equation. Solve over $[0,2\pi )$.
$$\cos x=\frac{1}{2}$$
The solution set is
(Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Step 1 ：The given equation is $\cos x=\frac{1}{2}$. We need to find the solutions over the interval $[0,2\pi )$.

Step 2 ：The cosine function is positive in the first and fourth quadrants of the unit circle. Therefore, we need to find the angles in these quadrants where the cosine is equal to 1/2.

Step 3 ：We know that $\cos (\pi /3)=1/2$ and $\cos (-\pi /3)=1/2$. However, since we are looking for solutions in the interval $[0,2\pi )$, we need to convert the negative angle to a positive angle by adding $2\pi$.

Step 4 ：Therefore, the solutions to the equation are $x=\pi /3$ and $x=2\pi -\pi /3$.

Step 5 ：In decimal form, these are approximately $x=1.047$ and $x=5.236$.

Step 6 ：Final Answer: The solutions to the equation $\cos x=\frac{1}{2}$ over the interval $[0,2\pi )$ are $x=\frac{\pi }{3}$ and $x=2\pi -\frac{\pi }{3}$. Therefore, the solution set is $\boxed{{\displaystyle \{\frac{\pi }{3},2\pi -\frac{\pi }{3}\}}}$.