Families in Radians

In radians a full turn is 2π. $\cos\left(x\right) = \frac{1}{2}$ has π/3 and 5π/3 in one turn, so every solution is

$$x = \frac{\pi}{3}+2\pi\cdot k$$

$$x = \frac{5\pi}{3}+2\pi\cdot k$$

The second family is the same as −π/3 + 2πk: 5π/3 is −π/3 plus one turn. Books often write the pair as ±π/3 + 2πk. Any base works, as long as the period is 2π for sine and cosine and π for tangent.