From Förberedande kurs i matematik 1

In the unit circle's first quadrant, there is one angle whose sine value equals \displaystyle \frac{1}{2} and that is \displaystyle v={\pi }/{6}\;.

From the figures, we see that there is a further angle with the same sine value and it lies in the second quadrant. Because of symmetry, it makes the same angle with the negative \displaystyle x -axis as \displaystyle v={\pi }/{6}\; makes with the positive \displaystyle x -axis, i.e. the other angle is \displaystyle v=\pi -{\pi }/{6}\;={5\pi }/{6}\;