From Förberedande kurs i matematik 1

If we draw the angle \displaystyle \pi/5 on the unit circle, then it will have an x-coordinate that is equal to \displaystyle \cos \pi/5\,.

In the figures, we see also that the only other angle between \displaystyle 0 and \displaystyle 2\pi which has the same cosine value, i.e. same x-coordinate, is the angle \displaystyle v=-\pi/5+2\pi = 9\pi/5 on the opposite side of the x-axis.