Find the smallest positive root of the equation cos (2x) = 0.5.

The solution of the problem:
cos (2 * x) = 1/2.
The cosine is equal to 1/2 at the following points:

2 * x = Pi / 3 + 2 * Pi * k and 2 * x = (- Pi) / 3 + 2 * Pi * k;

k are non-negative integers.
The second point has a minus sign, therefore, it does not fit the problem statement.
We take the first point:
2 * x = Pi / 3 + 2 * Pi * k;
x = (Pi / 3 + 2 * Pi * k) / 2;
x = Pi / 6 + Pi * k.
Since we need to find the smallest positive root, we take k = 0.
x = Pi / 6 + Pi * 0;

x = Pi / 6.
In degrees: x = 30 degrees.
Answer: x = 30 degrees.