cosx=1/2

To solve the equation \(\cos x = \frac{1}{2}\), we need to find the values of \(x\) that satisfy this equation.

The cosine function equals \(\frac{1}{2}\) at two standard angles in the interval \([0, 2\pi)\):

1. \(x = \frac{\pi}{3}\) (or 60 degrees)
2. \(x = \frac{5\pi}{3}\) (or 300 degrees)

Since cosine is a periodic function with a period of \(2\pi\), the general solutions can be expressed as:

\[ x = \frac{\pi}{3} + 2k\pi \] and \[ x = \frac{5\pi}{3} + 2k\pi \]

where \(k\) is any integer.

In summary, the complete solution is:

\[ x = \frac{\pi}{3} + 2k\pi \quad \text{and} \quad x = \frac{5\pi}{3} + 2k\pi, \quad k \in \mathbb{Z} \]